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A125818
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a(n)=((1 + 3Sqrt[2])^n + (1 - 3Sqrt[2])^n)/(2).
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4
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1, 1, 19, 55, 433, 1801, 10963, 52543, 291457, 1476145, 7907059, 40908583, 216237169, 1127920249, 5931872371, 31038388975, 162918608257, 853489829089, 4476595998547, 23462519091607
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 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]
a(n-1) is the number of compositions of n when there are 1 type of 1 and 18 types of other natural numbers. [From Milan R. Janjic (agnus(AT)blic.net), Aug 13 2010]
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FORMULA
| 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
If p[1]=1, and p[i]=18, (i>1), and if A is Hessenberg matrix of order n If p[1]=1, and p[i]=18, (i>1), and if A is Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n+1)=det A. [From Milan R. Janjic (agnus(AT)blic.net), Apr 29 2010]
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MATHEMATICA
| Expand[Table[((1 + 3Sqrt[2])^n + (1 - 3Sqrt[2])^n)/(2), {n, 0, 30}]] (*Artur Jasinski*)
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CROSSREFS
| Cf. A125817.
Sequence in context: A069131 A124712 A126373 * A093362 A176413 A061973
Adjacent sequences: A125815 A125816 A125817 * A125819 A125820 A125821
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Dec 10 2006
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