OFFSET
0,10
COMMENTS
Number of partitions of n into distinct parts congruent to 1 or 3 mod 5.
FORMULA
G.f.: Product_{k>=1} (1 + x^A047219(k)).
a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(21/20) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 24 2018
EXAMPLE
a(14) = 3 because we have [13, 1], [11, 3] and [8, 6].
MATHEMATICA
nmax = 72; CoefficientList[Series[Product[(1 + x^(5 k + 1)) (1 + x^(5 k + 3)), {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 72; CoefficientList[Series[QPochhammer[-x, x^5] QPochhammer[-x^3, x^5], {x, 0, nmax}], x]
nmax = 72; CoefficientList[Series[Product[(1 + Boole[MemberQ[{1, 3}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 23 2018
STATUS
approved