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 A087219 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). 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA 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). EXAMPLE 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 +... PROG (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)); CROSSREFS Cf. A078932, A087218. Sequence in context: A141016 A024736 A024562 * A214952 A199296 A219229 Adjacent sequences:  A087216 A087217 A087218 * A087220 A087221 A087222 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 27 2003 STATUS approved

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