A108300 a(n+2) = 3*a(n+1) + a(n), with a(0) = 1, a(1) = 5.
1, 5, 16, 53, 175, 578, 1909, 6305, 20824, 68777, 227155, 750242, 2477881, 8183885, 27029536, 89272493, 294847015, 973813538, 3216287629, 10622676425, 35084316904, 115875627137, 382711198315, 1264009222082, 4174738864561, 13788225815765, 45539416311856
Offset: 0
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1000
- Sergio Falcon, The k-Fibonacci difference sequences, Chaos, Solitons & Fractals, Volume 87, June 2016, Pages 153-157.
- Tanya Khovanova, Recursive Sequences
- Vincent Vatter, Growth rates of permutation classes: from countable to uncountable, arXiv:1605.04297 [math.CO], 2016. (Mentions a signed version.)
- Index entries for linear recurrences with constant coefficients, signature (3,1).
Crossrefs
Programs
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Maple
seriestolist(series((-2*x-1)/(x^2-1+3*x), x=0,25));
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Mathematica
LinearRecurrence[{3,1},{1,5},40] (* Harvey P. Dale, Jul 04 2013 *) -
PARI
Vec((1 + 2*x)/(1 - 3*x - x^2) + O(x^30)) \\ Andrew Howroyd, Jun 05 2021
Formula
G.f.: (1 + 2*x)/(1 - 3*x - x^2).
a(n)*a(n-2) = a(n-1)^2 + 9*(-1)^n. - Roger L. Bagula, May 17 2010
a(n) = 3^n*Sum_{k=0..n} A374439(n, k)*(1/3)^k. - Peter Luschny, Jul 26 2024
Comments