OFFSET
0,2
COMMENTS
Number of partitions of n into distinct parts if there are two types of 1's and two types of 2's.
FORMULA
a(n) ~ exp(Pi*sqrt(n/3)) / (3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Jun 11 2020
MATHEMATICA
nmax = 50; CoefficientList[Series[(1 + x) (1 + x^2) Product[(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = (1/n) Sum[Sum[(-1)^(k/d + 1) If[d < 3, 2, 1] d, {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 50}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 07 2020
STATUS
approved