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Search: id:A015523
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| A015523 |
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Linear 2nd order recurrence. |
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+0
5
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| 0, 1, 3, 14, 57, 241, 1008, 4229, 17727, 74326, 311613, 1306469, 5477472, 22964761, 96281643, 403668734, 1692414417, 7095586921, 29748832848, 124724433149, 522917463687, 2192374556806, 9191710988853, 38537005750589
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n) = 3 a(n-1) + 5 a(n-2).
a(n)=(3/2+sqrt(29)/2)^n/sqrt(29)-(3/2-sqrt(29)/2)^n/sqrt(29); a(n)=sum{k=0..floor((n-1)/2), binomial(n-k-1, k)5^k*3^(n-2k-1). - Paul Barry (pbarry(AT)wit.ie), Jul 20 2004
G.f.: -x/(-1+3*x+5*x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 16 2007
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PROGRAM
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(Other) sage: [lucas_number1(n, 3, -5) for n in xrange(0, 24)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
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Sequence in context: A037793 A037093 A135926 this_sequence A127363 A133444 A126875
Adjacent sequences: A015520 A015521 A015522 this_sequence A015524 A015525 A015526
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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