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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^k-1)/3).
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1
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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
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OFFSET
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0,2
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LINKS
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FORMULA
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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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PROG
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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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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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