%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