A108480 Expansion of (1-x-2*x^2)/(1-2*x-3*x^2-4*x^3+4*x^4).
1, 1, 3, 13, 35, 117, 379, 1197, 3859, 12357, 39563, 126845, 406371, 1302101, 4172443, 13369293, 42838835, 137266917, 439837739, 1409354397, 4515934339, 14470215157, 46366299963, 148569565165, 476055153491, 1525403341701
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (2,3,4,-4).
Programs
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Mathematica
CoefficientList[Series[(1-x-2*x^2)/(1-2*x-3*x^2-4*x^3+4*x^4), {x, 0, 20}], x] (* Vaclav Kotesovec, Jul 24 2013 *) LinearRecurrence[{2,3,4,-4},{1,1,3,13},30] (* Harvey P. Dale, Aug 29 2023 *)
Formula
a(n) = 2*a(n-1) + 3*a(n-2) + 4*a(n-3) - 4*a(n-4).
a(n) = Sum_{k=0..floor(n/2)} C(2*(n-k), 2k) * 2^k.
a(n) ~ (1+sqrt((4*sqrt(2)-1)/31)) * (1+2*sqrt(2)+sqrt(1+4*sqrt(2)))^n/2^(n+2). - Vaclav Kotesovec, Jul 24 2013