A108484 a(n) = Sum_{k=0..floor(n/2)} binomial(2n-2k,2k) * 3^(n-k).

1, 1, 4, 19, 55, 220, 793, 2845, 10480, 37963, 138259, 503608, 1831969, 6669865, 24276892, 88362451, 321640831, 1170726484, 4261339801, 15510894949, 56458080328, 205502135851, 748007984827, 2722677076336, 9910284168961

Offset

0,3

Comments

In general, Sum_{k=0..floor(n/2)} C(2n-2k,2k)a^k*b^(n-k) has expansion (1-bx-abx^2)/(1-2bx-(2ab-b^2)x^2-2ab^2*x^3+(ab)^2*x^4).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,5,6,-9).

Formula

G.f.: (1-x-3x^2)/(1-2x-5x^2-6x^3+9x^4).

a(n) = 2a(n-1)+5a(n-2)+6a(n-3)-9a(n-4).

Crossrefs

Cf. A108485, A108486, A108487.

Sequence in context: A215862 A174612 A020496 * A283333 A332697 A134507

Adjacent sequences: A108481 A108482 A108483 * A108485 A108486 A108487

Keyword

easy,nonn

Author

Paul Barry, Jun 04 2005

Status

approved