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A133345
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a(n)=2a(n-1)+14a(n-2) for n>1, a(0)=1, a(1)=1 .
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4
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1, 1, 16, 46, 316, 1276, 6976, 31816, 161296, 768016, 3794176, 18340576, 89799616, 436367296, 2129929216, 10369000576, 50557010176, 246280028416, 1200358199296, 5848636796416, 28502288382976, 138885491915776
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Binomial transform of A001024 (powers of 15), with interpolated zeros .
a(n) is the number of compositions of n when there are 1 type of 1 and 15 types of other natural numbers. [From Milan R. Janjic (agnus(AT)blic.net), Aug 13 2010]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,14).
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FORMULA
| G.f.: (1-x)/(1-2x-14x^2).
a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*15^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 26 2007
a(n)=(1/2)*[1-sqrt(15)]^n+(1/2)*[1+sqrt(15)]^n, n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 10 2008
If p[1]=1, and p[i]=15, (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)=det A. [From Milan R. Janjic` (agnus(AT)blic.net), Apr 29 2010]
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PROG
| (PARI) Vec((1-x)/(1-2*x-14*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012
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CROSSREFS
| Sequence in context: A099003 A124709 A126370 * A204616 A204800 A194268
Adjacent sequences: A133342 A133343 A133344 * A133346 A133347 A133348
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KEYWORD
| nonn,easy
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 21 2007
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