A099432 Convolution of A030195(n) (generalized (3,3)-Fibonacci) with itself.

1, 6, 33, 162, 756, 3402, 14931, 64314, 273051, 1145988, 4764744, 19656756, 80561061, 328316814, 1331513397, 5377120038, 21633427836, 86747114430, 346810621815, 1382826606210, 5500378861551, 21830478128136, 86469557676048

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (6,-3,-18,-9).

Formula

G.f.: 1/(1 - 3*x - 3*x^2)^2.

a(n) = 6*a(n-1) - 3*a(n-2) - 18*a(n-3) - 9*a(n-4). [corrected by Harvey P. Dale, May 20 2011]

a(n) = Sum_{k=0..floor((n+2)/2)} k*binomial(n-k+2, k)*3^(n-k+1).

a(n) = (sqrt(7)*n + 2*sqrt(7) - sqrt(3))*(5*sqrt(7)/98 + sqrt(3)/14)*(3*sqrt(21)/2 + 15/2)^(n/2) + (15/2 - 3*sqrt(21)/2)^(n/2)*(sqrt(7)*n + 2*sqrt(7) + sqrt(3))*(5*sqrt(7)/98 - sqrt(3)/14)*(-1)^n.

Mathematica

LinearRecurrence[{6, -3, -18, -9}, {1, 6, 33, 162}, 30] (* Harvey P. Dale, May 20 2011 *)

Crossrefs

Cf. A073388.

Sequence in context: A301272 A290921 A240880 * A072260 A281930 A282371

Adjacent sequences: A099429 A099430 A099431 * A099433 A099434 A099435

Keyword

easy,nonn

Author

Paul Barry, Oct 15 2004

Status

approved