

A133345


a(n)=2a(n1)+14a(n2) 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
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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.: (1x)/(12x14x^2).
a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*15^(nk).  Philippe Deléham, Dec 26 2007
a(n)=(1/2)*[1sqrt(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[ji+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((1x)/(12*x14*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



