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A102902 a(n)=9a(n-1)-16a(n-2). 1
1, 9, 65, 441, 2929, 19305, 126881, 833049, 5467345, 35877321, 235418369, 1544728185, 10135859761, 66507086889, 436390025825, 2863396842201, 18788331166609, 123280631024265, 808912380552641, 5307721328585529 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..1221

R. Flórez, R. A. Higuita, A. Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014).

Index entries for linear recurrences with constant coefficients, signature (9,-16).

FORMULA

G.f.: 1/(1-9x+16x^2); a(n)=sum{k=0..n, binomial(2n-k+1, k)4^k}; a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-16)^k*9^(n-2k)}.

a(n)=-(9/34)*[9/2-(1/2)*sqrt(17)]^n*sqrt(17)+(9/34)*sqrt(17)*[9/2+(1/2)*sqrt(17)]^n+(1/2)*[9/2 -(1/2)*sqrt(17)]^n+(1/2)*[9/2+(1/2)*sqrt(17)]^n, with n>=0 - Paolo P. Lava, Jun 16 2008

MATHEMATICA

Join[{a=1, b=9}, Table[c=9*b-16*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011*)

LinearRecurrence[{9, -16}, {1, 9}, 20] (* Harvey P. Dale, Jul 28 2016 *)

PROG

(Sage) [lucas_number1(n, 9, 16) for n in xrange(1, 21)]# [From Zerinvary Lajos, Apr 23 2009]

CROSSREFS

Cf. A002540, A099459.

Sequence in context: A237040 A055284 A081040 * A127534 A037548 A238275

Adjacent sequences:  A102899 A102900 A102901 * A102903 A102904 A102905

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jan 17 2005

STATUS

approved

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Last modified July 22 08:36 EDT 2017. Contains 289648 sequences.