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A260890
The number of overpartitions of n with restricted odd differences.
3
1, 1, 3, 3, 8, 9, 18, 21, 39, 46, 78, 93, 150, 180, 276, 333, 494, 597, 858, 1038, 1458, 1764, 2424, 2931, 3960, 4783, 6360, 7671, 10068, 12123, 15720, 18894, 24249, 29088, 36978, 44268, 55808, 66672, 83406, 99435, 123540, 146973, 181440, 215406, 264390, 313236, 382404, 452130, 549258
OFFSET
0,3
COMMENTS
The number of overpartitions of n where (i) the difference between successive parts may be odd only if the larger is overlined and (ii) if the smallest part is overlined, then it is odd.
LINKS
K. Bringmann, J. Dousse, J. Lovejoy, and K. Mahlburg, Overpartitions with restricted odd differences, Electron. J. Combin. 22 (2015), no.3, paper 3.17.
FORMULA
G.f.: Product_{n >= 1} (1-q^(3*n))/((1-q^n)*(1-q^(2*n))).
a(n) ~ sqrt(21) * exp(Pi*sqrt(7*n)/3) / (36*n). - Vaclav Kotesovec, Jun 13 2019
MAPLE
with(numtheory):
a:= proc(n) option remember;
`if`(n=0, 1, add(add(d*[1, 1, 2, 0, 2, 1]
[irem(d, 6)+1], d=divisors(j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..60); # Alois P. Heinz, Aug 08 2015
MATHEMATICA
QP = QPochhammer; QP[q^3]/(QP[q] QP[q^2]) + O[q]^50 // CoefficientList[#, q]& (* Jean-François Alcover, Mar 23 2017 *)
CROSSREFS
Sequence in context: A363125 A335602 A092549 * A022663 A304967 A323654
KEYWORD
nonn,changed
AUTHOR
Jeremy Lovejoy, Aug 06 2015
STATUS
approved