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A133345 a(n)=2a(n-1)+14a(n-2) for n>1, a(0)=1, a(1)=1. 6
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; text; internal format)
OFFSET

0,3

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 Janjic, Aug 13 2010]

LINKS

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (2,14).

FORMULA

G.f.: (1-x)/(1-2x-14x^2).

a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*15^(n-k). - Philippe Deléham, Dec 26 2007

a(n)=(1/2)*[1-sqrt(15)]^n+(1/2)*[1+sqrt(15)]^n, n>=0 - Paolo P. Lava, 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. - Milan Janjic, Apr 29 2010

MATHEMATICA

LinearRecurrence[{2, 14}, {1, 1}, 30] (* Harvey P. Dale, Jan 07 2016 *)

PROG

(PARI) Vec((1-x)/(1-2*x-14*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012

CROSSREFS

Sequence in context: A244094 A235549 A126370 * A253231 A253350 A204616

Adjacent sequences:  A133342 A133343 A133344 * A133346 A133347 A133348

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Dec 21 2007

STATUS

approved

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Last modified December 7 03:27 EST 2019. Contains 329836 sequences. (Running on oeis4.)