cp's OEIS Frontend

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.

%I A342911 #8 Jul 30 2023 17:42:35
%S A342911 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,
%T A342911 481,622,0,1,128,479,872,1265,1658,2051,0,1,256,1155,2254,3361,4468,
%U A342911 5575,6682,0,1,512,2787,5854,8993,12132,15271,18410,21549
%N 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.
%e A342911 Triangle starts:
%e A342911 [0] 1
%e A342911 [1] 0, 1
%e A342911 [2] 0, 1, 4
%e A342911 [3] 0, 1, 8,   15
%e A342911 [4] 0, 1, 16,  35,   54
%e A342911 [5] 0, 1, 32,  83,   134,  185
%e A342911 [6] 0, 1, 64,  199,  340,  481,  622
%e A342911 [7] 0, 1, 128, 479,  872,  1265, 1658,  2051
%e A342911 [8] 0, 1, 256, 1155, 2254, 3361, 4468,  5575,  6682
%e A342911 [9] 0, 1, 512, 2787, 5854, 8993, 12132, 15271, 18410, 21549
%p A342911 T := (n, k) -> `if`(n=0, 1, add((1+2*cos(j*Pi/(k+1)))^n, j=1..k)):
%p A342911 seq(seq(simplify(T(n, k)), k=0..n), n=0..8);
%Y A342911 Cf. A090326, A124696.
%K A342911 nonn,tabl
%O A342911 0,6
%A A342911 _Peter Luschny_, Mar 28 2021