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Search: id:A100227
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| 1, 1, 5, 13, 33, 81, 197, 477, 1153, 2785, 6725, 16237, 39201, 94641, 228485, 551613, 1331713, 3215041, 7761797, 18738637, 45239073, 109216785, 263672645, 636562077, 1536796801, 3710155681, 8957108165, 21624372013, 52205852193
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OFFSET
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0,3
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FORMULA
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a(n) = 2*a(n-1) + a(n-2) + 2 for n>1, with a(0)=1, a(1)=1. G.f.: Sum_{n>=1} a(n)*x^n/n = log((1-x)/(1-2*x-x^2)).
G.f.: (1-2*x+3*x^2)/(1-3*x+x^2+x^3). - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 22 2005
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PROGRAM
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(PARI) a(n)=if(n==0, 1, n*polcoeff(log((1-x)/(1-2*x-x^2)+x*O(x^n)), n))
(PARI) a(n)=polcoeff((1-2*x+3*x^2)/(1-3*x+x^2+x^3)+x*O(x^n), n) (Hanna)
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CROSSREFS
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Cf. A100225, A100226.
Equals A002203(n) - 1.
Adjacent sequences: A100224 A100225 A100226 this_sequence A100228 A100229 A100230
Sequence in context: A066184 A001981 A141025 this_sequence A027051 A109786 A055426
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 29 2004
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