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 A184894 a(n) equals the coefficient of x^(2n-1) in the n-th iteration of x+x^3 for n>=1. 1
 1, 2, 9, 78, 1045, 19320, 458304, 13306902, 457649757, 18202765482, 822272600160, 41592018711672, 2329051560965532, 143045976577538632, 9561491720518777632, 690994864767311671302, 53688078414653072521485, 4462898094035056790939070 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA Conjecture: a(m) = 0 (mod 3) everywhere except at m = (3^n+1)/2, n>=0. EXAMPLE The coefficients of x^(2k-1), k>=1, in the n-th iterations of x+x^3 begin: n=1: [(1), 1, 0, 0, 0, 0, 0, 0, ...]; n=2: [1,(2), 3, 3, 1, 0, 0, 0, ...]; n=3: [1, 3,(9), 24, 54, 102, 156, 192, ...]; n=4: [1, 4, 18,(78), 315, 1182, 4107, 13215, ...]; n=5: [1, 5, 30, 180,(1045), 5835, 31269, 160824, ...]; n=6: [1, 6, 45, 345, 2610,(19320), 139524, 982356, ...]; n=7: [1, 7, 63, 588, 5481, 50505,(458304), 4090128, ...]; n=8: [1, 8, 84, 924, 10234, 112812, 1232070,(13306902), ...]; ...; coefficients in parenthesis form the initial terms of this sequence. The nonzero terms (mod 3) begin: a(1)=1, a(2)=2, a(5)=2, a(14)=1, a(41)=2, a(122)=1, ... PROG (PARI) {a(n)=local(A=x, G=x+x^3); for(i=1, n, A=subst(G, x, A+x*O(x^(2*n)))); polcoeff(A, 2*n-1)} CROSSREFS Cf. A184900. Sequence in context: A192551 A121131 A166891 * A111196 A229211 A056918 Adjacent sequences:  A184891 A184892 A184893 * A184895 A184896 A184897 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 01 2011 STATUS approved

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Last modified April 10 20:07 EDT 2021. Contains 342856 sequences. (Running on oeis4.)