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A015536
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Expansion of x/(1-5*x-3*x^2).
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12
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0, 1, 5, 28, 155, 859, 4760, 26377, 146165, 809956, 4488275, 24871243, 137821040, 763718929, 4232057765, 23451445612, 129953401355, 720121343611, 3990466922120, 22112698641433, 122534893973525, 679012565791924
(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 (5,3).
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FORMULA
| a(n) = 5 a(n-1) + 3 a(n-2).
a(n)=(5/2+sqrt(37)/2)^n/sqrt(37)-(5/2-sqrt(37)/2)^n/sqrt(37); a(n)=sum{k=0..floor((n-1)/2), binomial(n-k-1, k)3^k*5^(n-2k-1). - Paul Barry (pbarry(AT)wit.ie), Jul 20 2004
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=5*b+3*a; a=b; b=c, {n, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 16 2011*)
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PROG
| (Other) sage: [lucas_number1(n, 5, -3) for n in xrange(0, 22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 24 2009]
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CROSSREFS
| Sequence in context: A037682 A126699 A164537 * A005785 A027912 A090040
Adjacent sequences: A015533 A015534 A015535 * A015537 A015538 A015539
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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