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

1,1

Links

Table of n, a(n) for n=1..63.

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

Formula

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

Example

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],
...

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;

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.

Sequence in context: A345298 A279350 A278221 * A336093 A304213 A129178

Adjacent sequences: A287876 A287877 A287878 * A287880 A287881 A287882

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jun 18 2017

Status

approved