OFFSET
0,10
COMMENTS
Number of partitions of n into distinct parts congruent to 2 or 3 mod 4.
FORMULA
G.f.: Product_{k>=1} (1 + x^A042964(k)).
a(n) ~ exp(Pi*sqrt(n/6)) / (4*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 23 2018
EXAMPLE
a(13) = 3 because we have [11, 2], [10, 3] and [7, 6].
MATHEMATICA
nmax = 70; CoefficientList[Series[Product[(1 + x^(4 k + 2)) (1 + x^(4 k + 3)), {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 70; CoefficientList[Series[QPochhammer[-x^2, x^4] QPochhammer[-x^3, x^4], {x, 0, nmax}], x]
nmax = 70; CoefficientList[Series[Product[(1 + Boole[MemberQ[{2, 3}, Mod[k, 4]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 22 2018
STATUS
approved