A184894 a(n) equals the coefficient of x^(2n-1) in the n-th iteration of x+x^3 for n>=1.

1, 2, 9, 78, 1045, 19320, 458304, 13306902, 457649757, 18202765482, 822272600160, 41592018711672, 2329051560965532, 143045976577538632, 9561491720518777632, 690994864767311671302, 53688078414653072521485, 4462898094035056790939070

Offset

1,2

Links

Table of n, a(n) for n=1..18.

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