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Search: id:A087223
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| A087223 |
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G.f. satisfies A(x) = f(x) + x*A(x)*f(x)^3, where f(x)=sum(k>=0,x^((4^n-1)/3)). |
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+0
2
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| 1, 2, 5, 14, 36, 96, 254, 676, 1792, 4756, 12621, 33490, 88868, 235818, 625764, 1660510, 4406296, 11692452, 31026836, 82332140, 218474784, 579739960, 1538385398, 4082226194, 10832507040, 28744906148, 76276860598, 202406625820
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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a(n) = A087221(3n+1).
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EXAMPLE
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Given f(x) = 1 +x +x^5 +x^21 +x^85 +x^341 +...
so that f(x)^3 = 1 +3x +3x^2 +x^3 +3x^5 +6x^6 +3x^7 +3x^10 +...
then A(x) = (1+x+x^5+...) + x*A(x)*(1+3x+3x^2+x^3+3x^5+6x^6 +...)
= 1 +2x +5x^2 +14x^3 +36x^4 +96x^5 +254x^6 +...
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PROGRAM
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(PARI) a(n)=local(A, m); if(n<1, n==0, m=1; A=1+O(x); while(m<=3*n+3, m*=4; A=1/(1/subst(A, x, x^4)-x)); polcoeff(A, 3*n+1))
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CROSSREFS
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Cf. A087221, A087222, A087224.
Sequence in context: A131408 A137917 A102714 this_sequence A005955 A062197 A030016
Adjacent sequences: A087220 A087221 A087222 this_sequence A087224 A087225 A087226
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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), Aug 27 2003
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