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Search: id:A125818
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| A125818 |
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a(n)=((1 + 3Sqrt[2])^n + (1 - 3Sqrt[2])^n)/(2). |
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+0
3
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| 1, 1, 19, 55, 433, 1801, 10963, 52543, 291457, 1476145, 7907059, 40908583, 216237169, 1127920249, 5931872371, 31038388975, 162918608257, 853489829089, 4476595998547, 23462519091607
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OFFSET
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1,3
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COMMENT
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Binomial transform of [1, 0, 18, 0, 324, 0, 5832, 0, 104976, 0, ...] =: powers of 18 (A001027) with interpolated zeros . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 02 2008]
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FORMULA
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a(0)=1, a(1)=1, a(n)=2*a(n-1)+17*a(n-2) for n>=2 . G.f.:(1-x)/(1-2*x-17*x^2) - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 12 2006
a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*18^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 26 2007
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MATHEMATICA
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Expand[Table[((1 + 3Sqrt[2])^n + (1 - 3Sqrt[2])^n)/(2), {n, 0, 30}]] (*Artur Jasinski*)
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CROSSREFS
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Cf. A125817.
Sequence in context: A069131 A124712 A126373 this_sequence A093362 A061973 A041702
Adjacent sequences: A125815 A125816 A125817 this_sequence A125819 A125820 A125821
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Dec 10 2006
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