A108480 Expansion of (1-x-2x^2)/(1-2x-3x^2-4x^3+4x^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

Author

Paul Barry, Jun 04 2005

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (2,3,4,-4).

Programs

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)=2a(n-1)+3a(n-2)+4a(n-3)-4a(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