OFFSET
0,6
FORMULA
a(n) = sum(k=0..n, T(n,k)), where T(n, m)=sum(i=1..(n-m)/3, binomial(m, i)*T((n-m)/3,i)), T(n,n)=1. - Vladimir Kruchinin, Mar 21 2015
G.f.: A(x)=1/B(x), where B(x) is g.f. of A290975. - Seiichi Manyama, Aug 18 2017
a(n) ~ c * d^n, where d = 1.391377080590304271048017099353... and c = 0.3625537262803710555422183139... - Vaclav Kotesovec, Aug 24 2017
EXAMPLE
G.f.: A(x) = 1 + x + x^2 + x^3 + x^4 + 2*x^5 + 3*x^6 + 4*x^7 + 5*x^8 +...
MATHEMATICA
nmax = 50; CoefficientList[Series[1/Fold[(1 - #2/#1) &, 1, Reverse[x^(Range[nmax + 1]^2)]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 24 2017 *)
PROG
(PARI) {a(n)=local(CF=1+x*O(x^n), M=sqrtint(n+1)); for(k=0, M, CF=1/(1-x^((M-k+1)^2)*CF)); polcoeff(CF, n, x)}
for(n=0, 55, print1(a(n), ", "))
(PARI) N = 66; q = 'q + O('q^N);
G(k) = if(k>N, 1, 1 - q^((k+1)^2) / G(k+1) );
gf = 1 / G(0);
Vec(gf) \\ Joerg Arndt, Jul 06 2013
(Maxima)
T(n, m):=if n=m then 1 else sum(binomial(m, i)*T((n-m)/3, i), i, 1, (n-m)/3);
makelist(sum(T(n, k), k, 0, n), n, 0, 20); /* Vladimir Kruchinin, Mar 21 2015 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 12 2012
STATUS
approved