OFFSET
0,3
COMMENTS
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..50
FORMULA
a(n) == 1 (mod 3).
EXAMPLE
G.f.: A(x) = 1 + x + 7*x^2 + 199*x^3 + 20026*x^4 + 7296946*x^5 +...
where
A(x)^3 = 1 + 3*x + 6*2^2*x^2 + 10*2^6*x^3 + 15*2^12*x^4 + 21*2^20*x^5 +...
more explicitly,
A(x)^3 = 1 + 3*x + 24*x^2 + 640*x^3 + 61440*x^4 + 22020096*x^5 +...+ A202944(n)*x^n +...
The residues modulo 2 of this sequence begin:
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,...];
which forms the characteristic function:
(1+x)*(1+x^2)*(1+x^8)*(1 + x^32 + x^128 + x^160 + x^512 + x^544 + x^640 + x^672 +...+ x^(32*A000695(n)) +...).
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, (m+1)*(m+2)/2*2^(m*(m-1))*x^m+x*O(x^n))^(1/3), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 26 2011
STATUS
approved