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A133356 a(n)=2a(n-1)+16a(n-2) for n>1, a(0)=1, a(1)=1 . 7
1, 1, 18, 52, 392, 1616, 9504, 44864, 241792, 1201408, 6271488, 31765504, 163874816, 835997696, 4293992448, 21963948032, 112631775232, 576686718976, 2955481841664, 15137951186944, 77563611840512, 397334442672128 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A001026 (powers of 17), with interpolated zeros .

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,16).

FORMULA

G.f.: (1-x)/(1-2x-16x^2).

a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*17^(n-k). - Philippe Deléham, Dec 26 2007

a(n)=(1/2)*[1-sqrt(17)]^n+(1/2)*[1+sqrt(17)]^n, n>=0 - Paolo P. Lava, Jun 10 2008

If p[1]=1, and p[i]=17, (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]

MATHEMATICA

LinearRecurrence[{2, 16}, {1, 1}, 30] (* Harvey P. Dale, Dec 12 2012 *)

PROG

(PARI) Vec((1-x)/(1-2*x-16*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jan 12 2012

CROSSREFS

Sequence in context: A299071 A124711 A126372 * A052495 A052902 A217591

Adjacent sequences:  A133353 A133354 A133355 * A133357 A133358 A133359

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Dec 21 2007

STATUS

approved

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Last modified September 20 05:51 EDT 2019. Contains 327212 sequences. (Running on oeis4.)