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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
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LINKS
| C. Dement, Floretion Multiplier
Index to sequences with linear recurrences with constant coefficients, signature (2,2,-2,-1)
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FORMULA
| 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.rs), May 30 2007
a(n) =n *sum_{k=1..n} sum_{i=ceil((n-k)/2)..n-k} binomial(i,n-k-i) *binomial(k+i-1,k-1) *(1-(-1)^k) /(2*k). - Vladimir Kruchinin, Apr 11 2011
a(n) = A001333(n+1)-A000035(n). - R. J. Mathar, Apr 12 2011
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PROG
| 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)
(Maxima)
a(n):=n*sum(sum(binomial(i, n-k-i)*binomial(k+i-1, k-1), i, ceiling((n-k)/2), n-k)*(1-(-1)^k)/(2*k), k, 1, n); /* Vladimir Kruchinin, Apr 11 2011 */
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CROSSREFS
| Cf. A113225, A002315, A082639, A100828.
Cf. A113281 - A113284.
Sequence in context: A065497 A131727 A073371 * A178945 A026571 A100099
Adjacent sequences: A113221 A113222 A113223 * A113225 A113226 A113227
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KEYWORD
| easy,nonn
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 18 2005
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