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.

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, 16, 38, 82, 123, 64, 1, 5, 8, 19, 48, 117, 244, 322, 128, 1, 5, 9, 22, 58, 152, 370, 730, 843, 256, 1, 6, 10, 25, 68

Offset: 3

Author

L. Edson Jeffery, Nov 23 2013

Keywords

• nonn
• tabl

Comments

Row indices n begin with 3, column indices k begin with 0.

Examples

			1,    1,    1,    1,    1,    1,    1,    1,    1,    1,    1,...
1,    2,    4,    8,   16,   32,   64,  128,  256,  512, 1024,...
2,    3,    7,   18,   47,  123,  322,  843, 2207, 5778,15127,...
2,    4,   10,   28,   82,  244,  730, 2188, 6562,19684,59050,...
		

Crossrefs

Cf. A186740, A185095, A198632, A198636.

Programs

Mathematica

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 *)

Formula

A(2*m+1,k) = A186740(m,k), m = 1,2,....

Conjecture: A(n,k) = floor(A198632(n-1,k)/2), n >= 3, k >= 0.