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Search: id:A105426
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| A105426 |
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a(0)=1, a(1)=5, a(n)=8*a(n-1)-a(n-2). |
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+0
2
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| 1, 5, 39, 307, 2417, 19029, 149815, 1179491, 9286113, 73109413, 575589191, 4531604115, 35677243729, 280886345717, 2211413522007, 17410421830339, 137071961120705, 1079165267135301, 8496250175961703, 66890836140558323
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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15*a(n)^2-14 is a square for all n.
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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G.f.: (1-3x)/(1-8x+x^2). a(n)=2*A105045(2*n+1)-1. a(-n)=2*A105045(2*n)-1, if n>0.
a(n)=(1/2)*[4-sqrt(15)]^n-(1/30)*[4-sqrt(15)]^n*sqrt(15)+(1/2)*[4+sqrt(15)]^n+(1/30)*sqrt(15) *[4+sqrt(15)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jul 08 2008
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PROGRAM
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(PARI) a(n)=subst(19*poltchebi(n)-poltchebi(n-1), x, 4)/15
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CROSSREFS
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Cf. a(n) = A001090(n+1) - 3*A001090(n).
Adjacent sequences: A105423 A105424 A105425 this_sequence A105427 A105428 A105429
Sequence in context: A053573 A003482 A135849 this_sequence A115187 A129763 A070767
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Apr 10 2005
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