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Search: id:A073708
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| A073708 |
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Generating function A(x) satisfies A(x)=((1+x)A(x^2))^2, A(0)=1. |
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+0
4
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| 1, 2, 5, 8, 18, 28, 50, 72, 129, 186, 301, 416, 664, 912, 1368, 1824, 2730, 3636, 5234, 6832, 9788, 12744, 17724, 24528, 35154, 48516, 65674, 90128, 121864, 159072, 203400, 267792, 346277, 443914, 549849, 703208, 875618, 1080860, 1294018
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The convolution of A073707, consisting of only the even terms of A073707.
First differences result in A073709={1, 1, 3, 3, 10, 10, 22, 22, 57, 57, 115, 115, ...}, the convolution of A073709 results in A073710={1, 2, 7, 12, 35, 58, 133, 208, ...}, which is the first differences of the unique terms of A073709.
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FORMULA
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G.f.: A(x) satisfies A(x)=((1+x)A(x^2))^2, A(0)=1.
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EXAMPLE
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(1 + x + 2x^2 + 2x^3 + 5x^4 + 5x^5 + 8x^6 + 8x^7 + 28x^8 + 28x^9 + ...)^2 = (1 + 2x + 5x^2 + 8x^3 + 18x^4 + 28x^5 + 50x^6 + 72x^7 + 129x^8 + ...).
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PROGRAM
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(PARI) a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=2; A=((1+x)*subst(A, x, x^2))^2); polcoeff(A, n))
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CROSSREFS
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Cf. A073709, A073710. A073707(2n)=a(n).
Sequence in context: A112361 A050872 A086324 this_sequence A024460 A039658 A063675
Adjacent sequences: A073705 A073706 A073707 this_sequence A073709 A073710 A073711
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KEYWORD
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easy,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 04 2002
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EXTENSIONS
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Edited by Michael Somos, May 03, 2003
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