A287879 Irregular triangle read by rows: normalized dimensions of certain generalized quadratic residue codes of length n.

2, 4, 2, 8, 6, 16, 16, 18, 32, 40, 50, 64, 96, 132, 146, 128, 224, 336, 406, 256, 512, 832, 1088, 1186, 512, 1152, 2016, 2832, 3330, 1024, 2560, 4800, 7200, 9060, 9762, 2048, 5632, 11264, 17952, 24024, 27654, 4096, 12288, 26112, 44032, 62352, 76176, 81330, 8192, 26624, 59904, 106496, 158912, 204984, 232050, 16384, 57344, 136192, 254464, 398720, 540736, 645540, 684210

Offset: 1

Author

N. J. A. Sloane, Jun 18 2017

Keywords

• nonn
• tabf

Examples

			Triangle begins:
[2],
[4, 2],
[8, 6],
[16, 16, 18],
[32, 40, 50],
[64, 96, 132, 146],
[128, 224, 336, 406],
[256, 512, 832, 1088, 1186],
[512, 1152, 2016, 2832, 3330],
[1024, 2560, 4800, 7200, 9060, 9762],
[2048, 5632, 11264, 17952, 24024, 27654],
[4096, 12288, 26112, 44032, 62352, 76176, 81330],
[8192, 26624, 59904, 106496, 158912, 204984, 232050],
[16384, 57344, 136192, 254464, 398720, 540736, 645540, 684210],
...
		

Links

• Harold N. Ward, Quadratic residue codes in their prime, Journal of Algebra, 150.1 (1992): 87-100. See Table I.

Crossrefs

The 0th column is A000079; column 1 is essentially the same as A057711 or A129952, and is also essentially twice A001792 or A049610.

Row sums are twice A287880.

Programs

Maple

g:=proc(m,w) local k;
if w=0 then 2^m else
2^m*add( (m/(m-w))*binomial(w-1,w-k)*binomial(m-w,k)/4^k, k=1..w);
fi;
end;
for n from 1 to 14 do
lprint( [seq(g(n,w),w=0..floor(n/2))]);
od;

Formula

See Ward, pp. 99-100, or the Maple code below.