c-gcc, 87 bytes

Result

WA

Code [DL]

s[9];main(j,t,a=48){for(;gets(s);puts(&a))for(j=t=strtol(s,0,2);j+1;j--)a+=j*j+j==t*2;}

stdin

10111100
11011111
10011001
10000111
00010010
01011000
10000110
00010101
11010010
00000101
00110110
00100100
11111101
00000000
10111111
11001101
01111000
00100000
01001110
01011011
00000011
11100111
00001010
10111011
10100010
00011100
01110110
11110101
11000011
10011100
10001101
00101011
01000010
00001111
11010010
11010111
00000110
10001000
10111110
00110011
00000001
01100111
00101101
10101011
00110111
00011100
10011011
01001111
01110011
01101001

stdout

stderr

/tmp/code.c:1:1: warning: data definition has no type or storage class
 s[9];main(j,t,a=48){for(;gets(s);puts(&a))for(j=t=strtol(s,0,2);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:1:16: error: expected ‘)’ before ‘=’ token
 s[9];main(j,t,a=48){for(;gets(s);puts(&a))for(j=t=strtol(s,0,2);j+1;j--)a+=j*j+j==t*2;}
                ^
/home/esolang/bin/c-gcc: line 6: /tmp/code: No such file or directory
rm: cannot remove '/tmp/code': No such file or directory

strace