A166868 Convolution of Jacobsthal(n+2) and Pell(n+1).

1, 5, 16, 48, 133, 357, 932, 2392, 6057, 15189, 37800, 93520, 230301, 565045, 1382236, 3373208, 8216033, 19980037, 48525632, 117730352, 285384437, 691295429, 1673567700, 4049615640, 9795168601, 23684692085, 57254031256

Offset: 0

Author

Paul Barry, Oct 22 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,1,-5,-2).

Programs

Mathematica

LinearRecurrence[{3, 1, -5, -2}, {1, 5, 16, 48}, 100] (* G. C. Greubel, May 27 2016 *)

Formula

G.f.: (1+2*x)/((1-x-2x^2)*(1-2x-x^2)).

a(n) = Sum{k=0..n} A001045(k+2)*A000129(n-k+1).

a(n) = 3*a(n-1) + a*(n-2) - 5*a(n-3) - 2*a(n-4).