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A102902
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a(n)=9a(n-1)-16a(n-2).
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0
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1, 9, 65, 441, 2929, 19305, 126881, 833049, 5467345, 35877321, 235418369, 1544728185, 10135859761, 66507086889, 436390025825, 2863396842201, 18788331166609, 123280631024265, 808912380552641, 5307721328585529
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..19.
Index to sequences with linear recurrences with constant coefficients, signature (9,-16).
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FORMULA
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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
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MATHEMATICA
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Join[{a=1, b=9}, Table[c=9*b-16*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 27 2011*)
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PROG
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(Sage) [lucas_number1(n, 9, 16) for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
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Cf. A002540, A099459.
Sequence in context: A020299 A055284 A081040 * A127534 A037548 A036731
Adjacent sequences: A102899 A102900 A102901 * A102903 A102904 A102905
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Jan 17 2005
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STATUS
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approved
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