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A102902 a(n)=9a(n-1)-16a(n-2). 0
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

Table of n, a(n) for n=0..19.

Index to sequences with 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*)

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 November 24 10:51 EST 2014. Contains 249895 sequences.