OFFSET
0,3
COMMENTS
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..200
EXAMPLE
G.f.: A(x) = 1 + x + 22*x^2 + 1624*x^3 + 264962*x^4 + 79136637*x^5 +...
where the coefficients of the cube of the g.f.
A(x)^3 = 1 + 3*x + 69*x^2 + 5005*x^3 + 806148*x^4 + 239220375*x^5 +...
satisfies:
1 = 1*(1-x)^3 + 3*x*(1-2^3*x+x^2)^3 + 69*x^2*(1-3^3*x+3^3*x^2-x^3)^3 + 5005*x^3*(1-4^3*x+6^3*x^2-4^3*x^3+x^4)^3 + 806148*x^4*(1-5^3*x+10^3*x^2-10^3*x^3+5^3*x^4-x^5)^3 +...
OBSERVATIONS.
The terms of this sequence are odd at positions:
[0, 1, 5, 21, 85, 341, ..., (4^k-1)/3, ...].
The terms of this sequence are congruent to 2 modulo 3 at positions:
[4,12,31,36,37,38,40,58,85,93,108,109,110,111,114,120,166,174,247,255,...].
The terms of A247031 are congruent to 2 modulo 3 at positions:
[12,36,93,108,111,114,120,174,255,279,324,327,330,333,342,360,...].
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 13 2014
STATUS
approved