A124717
Number of base 24 circular n-digit numbers with adjacent digits differing by 1 or less.
Original entry on oeis.org
1, 24, 70, 162, 434, 1154, 3160, 8732, 24394, 68634, 194300, 552752, 1579004, 4526364, 13014190, 37515722, 108392314, 313803194, 910109980, 2643790592, 7691092024, 22403591624, 65337858370, 190759113662, 557493641284
Offset: 0
A124718
Number of base 25 circular n-digit numbers with adjacent digits differing by 1 or less.
Original entry on oeis.org
1, 25, 73, 169, 453, 1205, 3301, 9125, 25501, 71773, 203253, 578405, 1652793, 4739305, 13630417, 39303329, 113588941, 328938125, 954262789, 2772787445, 8068471393, 23508942353, 68578993897, 200272341785, 585441977665
Offset: 0
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.
Original entry on oeis.org
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
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
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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);
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