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COMMENTS
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Generalized Fibonacci sequence.
Sqrt(26) = 10/2 + 10/101 + 10/(101*10301) + 10/(10301*1050601) + ... - Gary W. Adamson, Jun 13 2008
For positive n, a(n) equals the permanent of the n X n tridiagonal matrix with 10's along the main diagonal and 1's along the superdiagonal and the subdiagonal. - John M. Campbell, Jul 08 2011
a(n) equals the number of words of length n on alphabet {0, 1, ..., 10} avoiding runs of zeros of odd lengths. - Milan Janjic, Jan 28 2015
From Bruno Berselli, May 03 2018: (Start)
Numbers k for which m*k^2 + (-1)^k is a perfect square:
m = 2: 0, 1, 2, 5, 12, 29, 70, 169, ... (A000129);
m = 3: 0, 4, 56, 780, 10864, 151316, ... (4*A007655);
m = 5: 0, 1, 4, 17, 72, 305, 1292, ... (A001076);
m = 6: 0, 2, 20, 198, 1960, 19402, ... (A001078);
m = 7: 0, 48, 12192, 3096720, ... (2*A175672);
m = 8: 0, 6, 204, 6930, 235416, ... (A082405);
m = 10: 0, 1, 6, 37, 228, 1405, 8658, ... (A005668);
m = 11: 0, 60, 23880, 9504180, ... [°];
m = 12: 0, 2, 28, 390, 5432, 75658, ... (A011944);
m = 13: 0, 5, 180, 6485, 233640, ... (5*A041613);
m = 14: 0, 4, 120, 3596, 107760, ... (A068204);
m = 15: 0, 8, 496, 30744, 1905632, ... [°];
m = 17: 0, 1, 8, 65, 528, 4289, 34840, ... (A041025);
m = 18: 0, 4, 136, 4620, 156944, ... (A202299);
m = 19: 0, 13260, 1532829480, ... [°];
m = 20: 0, 2, 36, 646, 11592, 208010, ... (A207832);
m = 21: 0, 12, 1320, 145188, ... (A174745);
m = 22: 0, 42, 16548, 6519870, ... (A174766);
m = 23: 0, 240, 552480, 1271808720, ... [°];
m = 24: 0, 10, 980, 96030, 9409960, ... (A168520);
m = 26: 0, 1, 10, 101, 1020, 10301, ... (this sequence);
m = 27: 0, 260, 702520, 1898208780, ... [°];
m = 28: 0, 24, 6096, 1548360, ... (A175672);
m = 29: 0, 13, 1820, 254813, 35675640, ... [°];
m = 30: 0, 2, 44, 966, 21208, 465610, ... (2*A077421), etc.
[°] apparently without related sequences in the OEIS.
(End)
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