Search: id:A113224
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%I A113224
%S A113224 1,2,7,16,41,98,239,576,1393,3362,8119,19600,47321,114242,275807,665856,
%T A113224 1607521,3880898,9369319,22619536,54608393,131836322,318281039,
%U A113224 768398400,1855077841,4478554082,10812186007,26102926096,63018038201
%N A113224 a(2n) = A002315(n), a(2n+1) = A082639(n+1).
%C A113224 The logarithmic derivative of this sequence is twice 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
%D A113224 C. Dement, Floretion Integer Sequences (work in progress).
%F A113224 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)
%F A113224 Equals the self-convolution of integer sequence A113281. - Paul D. Hanna 
               (pauldhanna(AT)juno.com), Oct 22 2005
%F A113224 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.rs), May 30 2007
%o A113224 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
%o A113224 (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)
%Y A113224 Cf. A113225, A002315, A082639, A100828.
%Y A113224 Cf. A113281, A113282, A113283, A113284.
%Y A113224 Sequence in context: A065497 A131727 A073371 this_sequence A026571 A100099 
               A164267
%Y A113224 Adjacent sequences: A113221 A113222 A113223 this_sequence A113225 A113226 
               A113227
%K A113224 easy,nonn
%O A113224 0,2
%A A113224 Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 18 2005

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