Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Mar 19 2017 01:13:28
%S 1,1,1,2,2,1,2,3,4,1,3,4,7,8,1,3,5,10,18,16,1,4,6,13,28,47,32,1,4,7,
%T 16,38,82,123,64,1,5,8,19,48,117,244,322,128,1,5,9,22,58,152,370,730,
%U 843,256,1,6,10,25,68
%N Sequence read from antidiagonals of rectangular array given by A(n,k) = 2^(2*k)*(Sum_{j=1..n-floor(n/2)-1} (cos(j*Pi/n))^(2*k)), rows n >= 3, columns k >= 0.
%C Row indices n begin with 3, column indices k begin with 0.
%F A(2*m+1,k) = A186740(m,k), m = 1,2,....
%F Conjecture: A(n,k) = floor(A198632(n-1,k)/2), n >= 3, k >= 0.
%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
%e 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,...
%e 2, 3, 7, 18, 47, 123, 322, 843, 2207, 5778,15127,...
%e 2, 4, 10, 28, 82, 244, 730, 2188, 6562,19684,59050,...
%t Table[Function[m, FullSimplify[2^(2 k)*Sum[Cos[j*Pi/m]^(2 k), {j, m - Floor[m/2] - 1}]]][n - k + 1], {n, 3, 12}, {k, 0, n - 2}] // Flatten (* _Michael De Vlieger_, Mar 18 2017 *)
%Y Cf. A186740, A185095, A198632, A198636.
%K nonn,tabl
%O 3,4
%A _L. Edson Jeffery_, Nov 23 2013