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A232441 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.

%I A232441 #17 Mar 19 2017 01:13:28
%S A232441 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 A232441 16,38,82,123,64,1,5,8,19,48,117,244,322,128,1,5,9,22,58,152,370,730,
%U A232441 843,256,1,6,10,25,68
%N A232441 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 A232441 Row indices n begin with 3, column indices k begin with 0.
%F A232441 A(2*m+1,k) = A186740(m,k), m = 1,2,....
%F A232441 Conjecture: A(n,k) = floor(A198632(n-1,k)/2), n >= 3, k >= 0.
%e A232441 1,    1,    1,    1,    1,    1,    1,    1,    1,    1,    1,...
%e A232441 1,    2,    4,    8,   16,   32,   64,  128,  256,  512, 1024,...
%e A232441 2,    3,    7,   18,   47,  123,  322,  843, 2207, 5778,15127,...
%e A232441 2,    4,   10,   28,   82,  244,  730, 2188, 6562,19684,59050,...
%t A232441 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 A232441 Cf. A186740, A185095, A198632, A198636.
%K A232441 nonn,tabl
%O A232441 3,4
%A A232441 _L. Edson Jeffery_, Nov 23 2013