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Search: id:A082585
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| A082585 |
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a(1)=1, a(n)=ceiling(r(5)*a(n-1)) where r(5)= (1/2) *(5+sqrt(29)) is the positive root of X^2=5*X+1. |
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1
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| 1, 6, 32, 167, 868, 4508, 23409, 121554, 631180, 3277455, 17018456, 88369736, 458867137, 2382705422, 12372394248, 64244676663, 333595777564, 1732223564484, 8994713599985, 46705791564410, 242523671422036
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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n>3 a(n)=6*a(n-1)-4*a(n-2)-a(n-3); a(n)=floor(t(5)*r(5)^n) where t(5)=1/(10)*(1+7/sqrt(29)) is the positive root of 145*X^2=29*X+1
a(n)=-(1/5)+(3/5)*[5/2+(1/2)*sqrt(29)]^n+(16/145)*[5/2+(1/2)*sqrt(29)]^n*sqrt(29)+(3/5)*[5/2-(1/2) *sqrt(29)]^n-(16/145)*sqrt(29)*[5/2-(1/2)*sqrt(29)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 25 2008
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MAPLE
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a:=n->sum(fibonacci(i, 5), i=0..n): seq(a(n), n=1..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008
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CROSSREFS
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Cf. A000071, A048739, A082574, A049652.
Adjacent sequences: A082582 A082583 A082584 this_sequence A082586 A082587 A082588
Sequence in context: A034942 A046714 A129171 this_sequence A084326 A137637 A125190
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), May 07 2003
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