c-gcc, 86 bytes

Result

WA

Code [DL]

s;main(j,a,t){for(;gets(s);puts(&a))for(j=t=strtol(s,0,2),a=48;j+1;j--)a+=j*j+j==t*2;}

stdin

10001110
10001000
10111111
01101001
11111101
00100010
10001010
10001011
01001010
01110001
00100100
00001111
11111100
00011100
01011010
00000001
01010100
11001110
01011011
10111011
00110111
01111010
00101101
01010001
11000011
00010101
11001001
00011100
11010010
01001110
10101011
10011001
01110010
10111110
01111000
00000110
01000010
11010010
00001010
01001111
11110110
11110010
01011001
10011000
11011011
11111010
00000011
11100111
00000000
11010001

stdout

stderr

/tmp/code.c:1:1: warning: data definition has no type or storage class
 s;main(j,a,t){for(;gets(s);puts(&a))for(j=t=strtol(s,0,2),a=48;j+1;j--)a+=j*j+j==t*2;}
 ^
/tmp/code.c:1:1: warning: type defaults to ‘int’ in declaration of ‘s’ [-Wimplicit-int]
/tmp/code.c:1:3: warning: return type defaults to ‘int’ [-Wimplicit-int]
 s;main(j,a,t){for(;gets(s);puts(&a))for(j=t=strtol(s,0,2),a=48;j+1;j--)a+=j*j+j==t*2;}
   ^
/tmp/code.c: In function ‘main’:
/tmp/code.c:1:3: warning: type of ‘j’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:3: warning: type of ‘a’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:3: warning: type of ‘t’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:20: warning: implicit declaration of function ‘gets’ [-Wimplicit-function-declaration]
 s;main(j,a,t){for(;gets(s);puts(&a))for(j=t=strtol(s,0,2),a=48;j+1;j--)a+=j*j+j==t*2;}
                    ^
/tmp/code.c:1:28: warning: implicit declaration of function ‘puts’ [-Wimplicit-function-declaration]
 s;main(j,a,t){for(;gets(s);puts(&a))for(j=t=strtol(s,0,2),a=48;j+1;j--)a+=j*j+j==t*2;}
                            ^
/tmp/code.c:1:45: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 s;main(j,a,t){for(;gets(s);puts(&a))for(j=t=strtol(s,0,2),a=48;j+1;j--)a+=j*j+j==t*2;}
                                             ^
/tmp/cc5D740l.o: In function `main':
code.c:(.text.startup+0x19): warning: the `gets' function is dangerous and should not be used.
/home/esolang/bin/c-gcc: line 6:    13 Done                    cat -
        14 Segmentation fault      (core dumped) | /tmp/code

strace