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Search: id:A122120
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| A122120 |
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a(0)=1, a(1)=3, a(n)=4*a(n-1)+9*a(n-2) for n>1. |
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+0
1
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| 1, 3, 21, 111, 633, 3531, 19821, 111063, 622641, 3490131, 19564293, 109668351, 614752041, 3446023323, 19316861661, 108281656551, 606978381153, 3402448433571, 19072599164661, 106912432560783, 599303122725081
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OFFSET
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0,2
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COMMENT
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Binomial transform of A091914.
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FORMULA
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a(n)=Sum_{k, 0<=k<=n}3^(n-k)*A055380(n,k) . G.f.:(1-x)/(1-4*x-9*x^2) . a(n+1)/a(n) ->2+sqrt(13) if n -> infinity.
a(n)=-(1/26)*sqrt(13)*[2-sqrt(13)]^n+(1/2)*[2+sqrt(13)]^n+(1/26)*[2+sqrt(13)]^n*sqrt(13)+(1 /2)*[2-sqrt(13)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 19 2008]
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CROSSREFS
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Sequence in context: A140451 A054147 A043012 this_sequence A080952 A121140 A005057
Adjacent sequences: A122117 A122118 A122119 this_sequence A122121 A122122 A122123
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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 19 2006
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