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A106517 Convolution of Fib(n-1) and 3^n. 3
1, 3, 10, 31, 95, 288, 869, 2615, 7858, 23595, 70819, 212512, 637625, 1913019, 5739290, 17218247, 51655351, 154967040, 464902717, 1394710735, 4184136386, 12552415923, 37657258715, 112971793856, 338915410225, 1016746277043 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = A101220(2,3,n+1). - Ross La Haye, Jul 25 2005

LINKS

Table of n, a(n) for n=0..25.

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

FORMULA

G.f.: (1-x)/((1-x-x^2)(1-3x)); a(n)=sum{k=0..n, Fib(n-k-1)3^k}.

a(n) = A101220(3,3,n+1) - A101220(3,3,n). - Ross La Haye, May 31 2006

a(n) = (1/5)*(6*3^n - Lucas(n+1)). -- Ralf Stephan, Nov 16 2010

MATHEMATICA

LinearRecurrence[{4, -2, -3}, {1, 3, 10}, 30] (* Harvey P. Dale, Oct 08 2014 *)

CROSSREFS

Diagonal sums of number triangle A106516.

Sequence in context: A180432 A237930 A192337 * A055217 A097472 A068094

Adjacent sequences:  A106514 A106515 A106516 * A106518 A106519 A106520

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 05 2005

STATUS

approved

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Last modified February 21 00:32 EST 2018. Contains 299388 sequences. (Running on oeis4.)