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Search: id:A123270
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| A123270 |
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a(0)=1, a(1)=1, a(n)=5*a(n-1)+4*a(n-2). |
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+0
2
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| 1, 1, 9, 49, 281, 1601, 9129, 52049, 296761, 1692001, 9647049, 55003249, 313604441, 1788035201, 10194593769, 58125109649, 331403923321, 1889520055201, 10773215969289, 61424160067249, 350213664213401, 1996764961336001
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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First differences give {0, 8, 40, 232, 1320, 7528, 42920, ...} = 8*A015537(n) = 8 * {0, 1, 5, 29, 165, 941, 5365, ...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 03 2006
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FORMULA
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a(n)=Sum_{k, 0<=k<=n}4^(n-k)*A122542(n,k) . G.f. (1-4*x)/(1-5*x-4*x^2)
a(n) = 1 + 8*Sum[ A015537(k), {k,0,n} ]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 03 2006
a(n)=(1/2)*[5/2-(1/2)*sqrt(41)]^n-(3/82)*sqrt(41)*[5/2+(1/2)*sqrt(41)]^n+(3/82)*sqrt(41)*[5/2-(1 /2)*sqrt(41)]^n+(1/2)*[5/2+(1/2)*sqrt(41)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jul 07 2008
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CROSSREFS
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Cf. A015537.
Sequence in context: A081655 A055428 A012231 this_sequence A114040 A090390 A069665
Adjacent sequences: A123267 A123268 A123269 this_sequence A123271 A123272 A123273
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KEYWORD
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nonn
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 09 2006
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