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Search: id:A113224
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| 1, 2, 7, 16, 41, 98, 239, 576, 1393, 3362, 8119, 19600, 47321, 114242, 275807, 665856, 1607521, 3880898, 9369319, 22619536, 54608393, 131836322, 318281039, 768398400, 1855077841, 4478554082, 10812186007, 26102926096, 63018038201
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OFFSET
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0,2
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COMMENT
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The logarithmic derivative of this sequence is 2 times the g.f. of A113282, where a(2*n) = A113282(2*n), a(4*n+1) = A113282(4*n+1) - 3, a(4*n+3) = A113282(4*n+3) - 1. - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 22 2005
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REFERENCES
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C. Dement, Floretion Integer Sequences (work in progress).
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FORMULA
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G.f. (1+x^2)/((x-1)*(x+1)*(x^2+2*x-1), a(n+2) - a(n+1) - a(n) = A100828(n+1)
Equals the self-convolution of integer sequence A113281. - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 22 2005
a(n) = -(u^(n+1)-1)*(v^(n+1)-1)/2 with u = 1+sqrt(2), v = 1-sqrt(2). - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 30 2007
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PROGRAM
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Floretion Algebra Multiplication Program, FAMP Code: -2ibaseiseq[B*C], B = - .5'i + .5'j - .5i' + .5j' - 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj'; C = + .5'i + .5i' + .5'ii' + .5e
(PARI) {a(n)=local(x=X+X*O(X^n)); polcoeff((1+x^2)/(1-x^2)/(1-2*x-x^2), n, X)} (Hanna)
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CROSSREFS
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Cf. A113225, A002315, A082639, A100828.
Cf. A113281, A113282, A113283, A113284.
Sequence in context: A065497 A131727 A073371 this_sequence A026571 A100099 A000512
Adjacent sequences: A113221 A113222 A113223 this_sequence A113225 A113226 A113227
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KEYWORD
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easy,nonn
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 18 2005
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