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

3,4

Comments

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

Links

Table of n, a(n) for n=3..61.

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.

Example

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,...

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 *)

Crossrefs

Cf. A186740, A185095, A198632, A198636.

Sequence in context: A293520 A292602 A071444 * A328701 A085257 A352889

Adjacent sequences: A232438 A232439 A232440 * A232442 A232443 A232444

Keyword

nonn,tabl

Author

L. Edson Jeffery, Nov 23 2013

Status

approved