OFFSET
0,10
COMMENTS
Number of partitions of n into distinct parts congruent to 2 or 4 mod 5.
FORMULA
G.f.: Product_{k>=1} (1 + x^A047211(k)).
a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(29/20) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 24 2018
EXAMPLE
a(16) = 3 because we have [14, 2], [12, 4] and [9, 7].
MATHEMATICA
nmax = 74; CoefficientList[Series[Product[(1 + x^(5 k + 2)) (1 + x^(5 k + 4)), {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 74; CoefficientList[Series[QPochhammer[-x^2, x^5] QPochhammer[-x^4, x^5], {x, 0, nmax}], x]
nmax = 74; CoefficientList[Series[Product[(1 + Boole[MemberQ[{2, 4}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 23 2018
STATUS
approved