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A094688
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Convolution of Fibonacci(n) and 3^n.
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3
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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; internal format)
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OFFSET
| 0,3
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (4,-2,-3).
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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 (rlahaye(AT)new.rr.com), 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 (rlahaye(AT)new.rr.com), Aug 20 2005
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MATHEMATICA
| Join[{a = b = 0}, Table[c = 3^n + a + b; a = b; b = c, {n, 0, 100}]] (* From Vladimir Joseph Stephan Orlovsky, Jun 28 2011 *)
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PROG
| (PARI) a(n)=(3^(n+1)-fibonacci(n+1)-fibonacci(n+3))/5 \\ Charles R Greathouse IV, Jun 28 2011
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CROSSREFS
| Cf. A000032.
Sequence in context: A182902 A108765 A005775 * A068092 A153480 A171851
Adjacent sequences: A094685 A094686 A094687 * A094689 A094690 A094691
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 19 2004
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