OFFSET
1,2
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 01 2011
STATUS
approved