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A133343
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a(n)=2a(n-1)+13a(n-2) for n>1, a(0)=1, a(1)=1 .
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5
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1, 1, 15, 43, 281, 1121, 5895, 26363, 129361, 601441, 2884575, 13587883, 64675241, 305992961, 1452764055, 6883436603, 32652805921, 154790287681, 734067052335, 3480407844523, 16503687369401, 78252676717601
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OFFSET
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0,3
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COMMENTS
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Binomial transform of A001023 (powers of 14), with interpolated zeros .
a(n) is the number of compositions of n when there are 1 type of 1 and 14 types of other natural numbers. [From Milan Janjic, Aug 13 2010]
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LINKS
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Table of n, a(n) for n=0..21.
Index to sequences with linear recurrences with constant coefficients, signature (2,13).
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FORMULA
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G.f.: (1-x)/(1-2x-13x^2).
a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*14^(n-k). - Philippe DELEHAM, Dec 26 2007
a(n)=(1/2)*[1-sqrt(14)]^n+(1/2)*[1+sqrt(14)]^n, n>=0 - Paolo P. Lava, Jun 10 2008
If p[1]=1, and p[i]=14, (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 Janjic, Apr 29 2010]
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PROG
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(PARI) Vec((1-x)/(1-2*x-13*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012
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CROSSREFS
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Sequence in context: A204734 A126369 A193647 * A027845 A201810 A029827
Adjacent sequences: A133340 A133341 A133342 * A133344 A133345 A133346
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Philippe DELEHAM, Dec 21 2007
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STATUS
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approved
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