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A087219
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Satisfies A(x) = f(x) + x*A(x)*f(x)^2, where f(x)=sum(k>=0,x^((3^n-1)/2)) and f(x)^2 = 2 - f(x^2) + 2*sum(n>0,x^A023745(n)). Also, A(x) = f(x)*B(x), where B(x)=sum(k>=0, A087218(k)*x^k).
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2
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1, 2, 4, 9, 20, 44, 99, 219, 487, 1083, 2406, 5349, 11889, 26426, 58739, 130563, 290208, 645062, 1433814, 3187014, 7083951, 15745878, 34999212, 77794638, 172918335, 384354909, 854326387, 1898957331, 4220914872, 9382055124
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..29.
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FORMULA
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a(n)=A078932(2n+1). a(m)=1 (mod 3) when m=(3^n-1)/2 (mod 3), else a(m)=2 (mod 3) when m=A023745(n), otherwise a(m)=0 (mod 3).
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EXAMPLE
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Given f(x) = 1 +x +x^4 +x^13 +x^40 +x^121 +... so that f(x)^2 = 1 +2x +x^2 +2x^4 +2x^5 +x^8 +2*x^13 +... then A(x) = (1+x+x^4 +...) + x*A(x)*(1+2x+x^2+2x^4+2x^5+...) = 1 +2x +4x^2 +9x^3 +20x^4 +44x^5 +...
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PROG
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(PARI) a(n)=local(A, m); if(n<1, 1, m=1; A=1+O(x); while(m<=2*n+1, m*=3; A=1/(1/subst(A, x, x^3)-x)); polcoeff(A, 2*n+1));
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CROSSREFS
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Cf. A078932, A087218.
Sequence in context: A141016 A024736 A024562 * A214952 A199296 A219229
Adjacent sequences: A087216 A087217 A087218 * A087220 A087221 A087222
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Aug 27 2003
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STATUS
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approved
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