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

%I A287879 #18 Feb 04 2019 07:26:48
%S A287879 2,4,2,8,6,16,16,18,32,40,50,64,96,132,146,128,224,336,406,256,512,
%T A287879 832,1088,1186,512,1152,2016,2832,3330,1024,2560,4800,7200,9060,9762,
%U A287879 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
%N A287879 Irregular triangle read by rows: normalized dimensions of certain generalized quadratic residue codes of length n.
%H A287879 Harold N. Ward, <a href="https://doi.org/10.1016/S0021-8693(05)80051-1">Quadratic residue codes in their prime</a>, Journal of Algebra, 150.1 (1992): 87-100. See Table I.
%F A287879 See Ward, pp. 99-100, or the Maple code below.
%e A287879 Triangle begins:
%e A287879 [2],
%e A287879 [4, 2],
%e A287879 [8, 6],
%e A287879 [16, 16, 18],
%e A287879 [32, 40, 50],
%e A287879 [64, 96, 132, 146],
%e A287879 [128, 224, 336, 406],
%e A287879 [256, 512, 832, 1088, 1186],
%e A287879 [512, 1152, 2016, 2832, 3330],
%e A287879 [1024, 2560, 4800, 7200, 9060, 9762],
%e A287879 [2048, 5632, 11264, 17952, 24024, 27654],
%e A287879 [4096, 12288, 26112, 44032, 62352, 76176, 81330],
%e A287879 [8192, 26624, 59904, 106496, 158912, 204984, 232050],
%e A287879 [16384, 57344, 136192, 254464, 398720, 540736, 645540, 684210],
%e A287879 ...
%p A287879 g:=proc(m,w) local k;
%p A287879 if w=0 then 2^m else
%p A287879 2^m*add( (m/(m-w))*binomial(w-1,w-k)*binomial(m-w,k)/4^k, k=1..w);
%p A287879 fi;
%p A287879 end;
%p A287879 for n from 1 to 14 do
%p A287879 lprint( [seq(g(n,w),w=0..floor(n/2))]);
%p A287879 od;
%Y A287879 The 0th column is A000079; column 1 is essentially the same as A057711 or A129952, and is also essentially twice A001792 or A049610.
%Y A287879 Row sums are twice A287880.
%K A287879 nonn,tabf
%O A287879 1,1
%A A287879 _N. J. A. Sloane_, Jun 18 2017