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A155198
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a(n)=9*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=8, a(2)=72 .
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1
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1, 8, 72, 656, 5976, 54440, 495936, 4517864, 41156712, 374928272, 3415511160, 31114528712, 283446269568, 2582130954824, 23522624862984, 214285754721680, 1952094417358104, 17783135510944616, 162000314015859648
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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..18.
Index entries for linear recurrences with constant coefficients, signature (9,1).
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FORMULA
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G.f.: (1-x-x^2)/(1-9*x-x^2).
a(n)=4*{[(9/2)-(1/2)*sqrt(85)]^(n-1)+[(9/2)+(1/2)*sqrt(85)]^(n-1)}+(36/85)*sqrt(85)*{[(9/2)+(1/2)*sqrt(85)]^(n-1)-[(9/2)-(1/2)*sqrt(85)]^(n-1)}+[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava, Jan 26 2009]
a(n) = Sum_{k, 0<=k<=n} A155161(n,k)*8^k. - Philippe Deléham, Feb 08 2012
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MATHEMATICA
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LinearRecurrence[{9, 1}, {1, 8, 72}, 20] (* Harvey P. Dale, Aug 22 2016 *)
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CROSSREFS
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Sequence in context: A057091 A156566 A055275 * A147840 A115970 A078995
Adjacent sequences: A155195 A155196 A155197 * A155199 A155200 A155201
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KEYWORD
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nonn,easy
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AUTHOR
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Philippe Deléham, Jan 21 2009
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STATUS
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approved
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