A342911 T(n, k) = Sum_{j=1..k} (1 + 2*cos(j*Pi/(k + 1)))^n for n > 0, T(0, 0) = 1. Triangle read by rows, T(n, k) for 0 <= k <= n.

1, 0, 1, 0, 1, 4, 0, 1, 8, 15, 0, 1, 16, 35, 54, 0, 1, 32, 83, 134, 185, 0, 1, 64, 199, 340, 481, 622, 0, 1, 128, 479, 872, 1265, 1658, 2051, 0, 1, 256, 1155, 2254, 3361, 4468, 5575, 6682, 0, 1, 512, 2787, 5854, 8993, 12132, 15271, 18410, 21549

Offset: 0

Author

Peter Luschny, Mar 28 2021

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1
[1] 0, 1
[2] 0, 1, 4
[3] 0, 1, 8,   15
[4] 0, 1, 16,  35,   54
[5] 0, 1, 32,  83,   134,  185
[6] 0, 1, 64,  199,  340,  481,  622
[7] 0, 1, 128, 479,  872,  1265, 1658,  2051
[8] 0, 1, 256, 1155, 2254, 3361, 4468,  5575,  6682
[9] 0, 1, 512, 2787, 5854, 8993, 12132, 15271, 18410, 21549
		

Crossrefs

Cf. A090326, A124696.

Programs

Maple

T := (n, k) -> `if`(n=0, 1, add((1+2*cos(j*Pi/(k+1)))^n, j=1..k)):
seq(seq(simplify(T(n, k)), k=0..n), n=0..8);