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A099432 Convolution of A030195(n) (generalized (3,3)-Fibonacci) with itself. 1
1, 6, 33, 162, 756, 3402, 14931, 64314, 273051, 1145988, 4764744, 19656756, 80561061, 328316814, 1331513397, 5377120038, 21633427836, 86747114430, 346810621815, 1382826606210, 5500378861551, 21830478128136, 86469557676048 (list; graph; refs; listen; history; text; internal format)
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).

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

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

EXTENSIONS

Second formula corrected by Harvey P. Dale, May 20 2011.

STATUS

approved

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Last modified October 23 16:53 EDT 2018. Contains 316529 sequences. (Running on oeis4.)