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A094688 Convolution of Fibonacci(n) and 3^n. 5
0, 1, 4, 14, 45, 140, 428, 1297, 3912, 11770, 35365, 106184, 318696, 956321, 2869340, 8608630, 25826877, 77482228, 232449268, 697351985, 2092062720, 6276199106, 18828615029, 56485873744, 169457667600, 508373077825, 1525119354868 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f. : x/((1-3x)(1-x-x^2)); a(n)=3^(n+1)/5-L(n+2)/5; a(n)=4a(n-1)-2a(n-2)-3a(n-3).

a(n) = A101220(3, 3, n) - Ross La Haye, Jan 28 2005

a(0) = 0, a(1) = 1, a(n) = a(n-1) + a(n-2) + 3^(n-1) for n > 1. - Ross La Haye, Aug 20 2005

a(n) = (3^(n+1) - Lucas(n+2))/5, where Lucas = A000032. - Vladimir Reshetnikov, Sep 27 2016

MATHEMATICA

Join[{a = b = 0}, Table[c = 3^n + a + b; a = b; b = c, {n, 0, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jun 28 2011 *)

LinearRecurrence[{4, -2, -3}, {0, 1, 4}, 40] (* Vincenzo Librandi, Jun 24 2012 *)

Table[(3^(n+1) - LucasL[n+2])/5, {n, 0, 20}] (* Vladimir Reshetnikov, Sep 27 2016 *)

PROG

(PARI) a(n)=(3^(n+1)-fibonacci(n+1)-fibonacci(n+3))/5 \\ Charles R Greathouse IV, Jun 28 2011

(MAGMA) I:=[0, 1, 4]; [n le 3 select I[n] else 4*Self(n-1)-2*Self(n-2)-3*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 24 2012

CROSSREFS

Cf. A000032.

Sequence in context: A182902 A108765 A005775 * A068092 A255678 A153480

Adjacent sequences:  A094685 A094686 A094687 * A094689 A094690 A094691

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 19 2004

STATUS

approved

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Last modified February 24 06:13 EST 2018. Contains 299597 sequences. (Running on oeis4.)