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Search: id:A091190
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| A091190 |
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G.f. A(x) satisfies xA(x)^3 = B(xA(x^3)) where B(x) = x/(1-3x). |
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+0
3
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| 1, 1, 2, 5, 13, 35, 97, 273, 778, 2240, 6499, 18976, 55703, 164243, 486130, 1443620, 4299365, 12836825, 38413933, 115184282, 346005073, 1041072108, 3137060983, 9465689545, 28596915843, 86492865522, 261876842801, 793661873276
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OFFSET
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0,3
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COMMENT
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More generally, given A(x) satisfies xA(x)^p = B(xA(x^p)) where B(x) = x/(1-p*x), then it appears that A(x) is an integer series only when p is prime. This is a special case of sequences with g.f.s that satisfy the more general functional equation xA(x)^m = B(xA(x^m)) originated by Michael Somos; some other examples are A085748, A091188, and A091200.
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PROGRAM
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(PARI) {a(n)=local(A, m); p=3; if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=p; A=x*subst(A, x, x^p); A=(A/(1-p*A)/x)^(1/p)); polcoeff(A, n))}
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CROSSREFS
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Cf. A085748, A091188, A091200.
Adjacent sequences: A091187 A091188 A091189 this_sequence A091191 A091192 A091193
Sequence in context: A085810 A005773 A022855 this_sequence A007689 A085281 A082582
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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), Feb 22 2004
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 25 2006
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