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>>> ''.join(d=="1"and"0001000"or d for d in "000010000010000")
'000000010000000000010000000'

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1

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        !to "test.prg", cbm
        
        ptr     = $fa
        
        chrout  = $ffd2
        strout  = $ab1e
        
        * = $c000

start   lda #<vector
        ldy #>vector
        sta ptr
        sty ptr+1
        jsr strout
        lda #13
        jsr chrout
        
        ldx #0
loop    ldy #3
        lda (ptr),y
        beq done
        cmp #"1"
        bne +
        ldx #7
+       cpx #0
        beq ++
        lda #"1"
        dex
++      ldy #0
        sta (ptr),y
        inc ptr
        bne loop
        inc ptr+1
        bne loop

done    lda #<vector
        ldy #>vector
        jsr strout
        lda #13
        jmp chrout

vector  !pet "00001001000000001000000", 0

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       JIFFYDOS V6.01 (C)1989 CMD

 C-64 BASIC V2   38911 BASIC BYTES FREE

   CYBERPUNX RETRO REPLAY 64KB - 3.8P

READY.
LOAD"TEST.PRG",8,1

SEARCHING FOR TEST.PRG
LOADING $C000 $C055
READY.
SYS49152
00001001000000001000000
01111111111001111111000

READY.

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#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/* convvec.c - Convert Vector, compile with: 
   gcc -Wall -Wextra -ansi -pedantic convvec.c -o convvec */

char *convertvector(char *vector, int width);

int main() {
    char vector[16] = "000010000010000";
    puts(vector);
    puts(convertvector(vector, 3));
    return 0;
}

char *convertvector(char *vector, int width) {
    int i;
    int u;
    int ones[15];
    int oneindex;
    int tochange[15];
    int tochangeindex;
    int vectorlength;
    char *vectorp;
    oneindex = 0;
    tochangeindex = 0;
    vectorlength = strlen(vector);
    for(i = 0; i < vectorlength; i ++) {
        if(vector[i] == '1') {
            ones[oneindex] = i;
            oneindex++;
        }
    }
    for(i = 0; i < oneindex; i++) {
        for(u = 1; u <= width; u++) {
            tochange[tochangeindex] = ones[i] + u;
            tochangeindex++;
            tochange[tochangeindex] = ones[i] - u;
            tochangeindex++;
        }
    }
    for(i = 0; i < tochangeindex; i++) {
        vectorp = vector;
        if(tochange[i] >= 0) {
            vectorp += tochange[i];
            *vectorp = '1';
        }
    }
    return vector;
}

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#include <iso646.h>
#include <stdio.h>

#define HALF_WIDTH      3

void set_ones(char *vector)
{
    char c;
    unsigned int i, n = 0;
    
    for (i = 0; i < HALF_WIDTH and (c = vector[i]); ++i) {
        if (c == '1') n = HALF_WIDTH + i + 1;
    }
    for (i = 0; (c = vector[i + HALF_WIDTH]); ++i) {
        if (c == '1') n = HALF_WIDTH * 2 + 1;
        if (n) {
            vector[i] = '1';
            --n;
        }
    }
    while (n and vector[i]) {
        vector[i++] = '1';
        --n;
    }
}

int main(void)
{
    char vector[] = "00001001000000001000000";
    puts(vector);
    set_ones(vector);
    puts(vector);
    return 0;
}

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        .importzp   ptr1
        .export     _set_ones

        HALF_WIDTH = 3
; 
; void __fastcall__ set_ones(char *vector);
; 
.proc _set_ones
.code
        sta ptr1
        stx ptr1+1
        
        ldx #0
        ldy #$ff
        bne L2
loop1:  lda (ptr1),y
        beq loop2
        cmp #'1'
        bne L2
        tya
        clc
        adc #HALF_WIDTH + 1
        tax
L2:     iny
        cpy #HALF_WIDTH
        bne loop1

loop2:  ldy #HALF_WIDTH
        lda (ptr1),y
        beq endloop2
        cmp #'1'
        bne @skip1
        ldx #HALF_WIDTH * 2 + 1
@skip1: cpx #0
        beq @skip2
        dex
        lda #'1'
        ldy #0
        sta (ptr1),y
@skip2: inc ptr1
        bne loop2
        inc ptr1+1
        bne loop2
endloop2:

        ldy #0
loop3:  dex
        bmi endloop3
        lda (ptr1),y
        beq endloop3
        lda #'1'
        sta (ptr1),y
        iny
        bne loop3
endloop3:
        rts
.endproc

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#include <stdio.h>
#include <stdlib.h>
#include <string.h>

/* convvec.c - Convert Vector, compile with:
   gcc -Wall -Wextra -ansi -pedantic convvec.c -o convvec */

char *convertvector(char *vector, int width);

int main() {
    /* char vector[] = "000010000010000"; */
    char vector[] = "00001001000000001000000";
    puts(vector);
    puts(convertvector(vector, 3));
    return 0;
}

char *convertvector(char *vector, int width) {
    int i;
    int u;
    int vectorlength = strlen(vector);
    int *ones = malloc(vectorlength - 1);
    int oneindex;
    int *tochange = malloc(vectorlength - 1);
    int tochangeindex;
    oneindex = 0;
    tochangeindex = 0;
    for(i = 0; i < vectorlength; i ++) {
        if(vector[i] == '1') {
            ones[oneindex] = i;
            oneindex++;
        }
    }
    for(i = 0; i < oneindex; i++) {
        for(u = 1; u <= width; u++) {
            tochange[tochangeindex] = ones[i] + u;
            tochangeindex++;
            tochange[tochangeindex] = ones[i] - u;
            tochangeindex++;
        }
    }
    for(i = 0; i < tochangeindex; i++) {
        if(tochange[i] >= 0 && i < vectorlength) {
            vector[tochange[i]] = '1';
        }
    }
    return vector;
}

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>>> example = [0,0,0,0,1,0,0,0,0,0,1,0,0,0,0]
>>> size = 3
>>> map(int, map(any, zip(*[([0]*size+example+[0]*size)[i:] for i in range(2*size+1)])))
[0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0]

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   10 HW=3:V$="00001001000000001000000":LV=LEN(V$):PRINT V$
   20 DIM V$(LV):FOR I=0 TO LV:V$(I)=MID$(V$,I+1,1):NEXT
   30 N=0:FOR I=0 TO HW:IF V$(I)="1" THEN N=HW+1+I
   40 NEXT
   50 FOR I=0 TO LV-HW:IF V$(I+HW)="1" THEN N=HW*2+1
   60 IF N>0 THEN V$(I)="1":N=N-1
   70 NEXT
   80 IF N=0 OR I=LV THEN 100
   90 V$(I)="1":I=I+1:N=N-1:GOTO 80
  100 FOR I=0 TO LV:PRINT V$(I);:NEXT:PRINT