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A246584 Number of overcubic partitions of n. 7
1, 2, 6, 12, 26, 48, 92, 160, 282, 470, 784, 1260, 2020, 3152, 4896, 7456, 11290, 16836, 24962, 36556, 53232, 76736, 110012, 156384, 221156, 310482, 433776, 602200, 832224, 1143696, 1565088, 2131072, 2890266, 3902344, 5249356, 7032576 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of A001935 and A002513. - Vaclav Kotesovec, Aug 16 2019

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Michael D. Hirschhorn, A note on overcubic partitions, New Zealand J. Math., 42:229-234, 2012.

Bernard L. S. Lin, Arithmetic properties of overcubic partition pairs, Electronic Journal of Combinatorics 21(3) (2014), #P3.35.

James A. Sellers, Elementary proofs of congruences for the cubic and overcubic partition functions, Australasian Journal of Combinatorics, 60(2) (2014), 191-197.

FORMULA

G.f.: Product_{k>=1} (1+x^k) * (1+x^(2*k)) / ((1-x^k) * (1-x^(2*k))). - Vaclav Kotesovec, Aug 16 2019

a(n) ~ 3^(3/4) * exp(sqrt(3*n/2)*Pi) / (2^(19/4)*n^(5/4)). - Vaclav Kotesovec, Aug 16 2019

MAPLE

# to get 140 terms:

ph:=add(q^(n^2), n=-12..12);

ph:=series(ph, q, 140);

g1:=1/(subs(q=-q, ph)*subs(q=-q^2, ph));

g1:=series(g1, q, 140);

seriestolist(%);

# second Maple program:

with(numtheory):

a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(d*

      `if`(irem(d, 4)=2, 3, 2), d=divisors(j)), j=1..n)/n)

    end:

seq(a(n), n=0..40);  # Alois P. Heinz, Aug 17 2019

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1+x^k) * (1+x^(2*k)) / ((1-x^k) * (1-x^(2*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 16 2019 *)

nmax = 50; CoefficientList[Series[Product[(1+x^(2*k)) / (1-x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 16 2019 *)

CROSSREFS

Trisections: A246585, A246586, A246587.

Sequence in context: A136515 A141347 A300120 * A054454 A084170 A245264

Adjacent sequences:  A246581 A246582 A246583 * A246585 A246586 A246587

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 03 2014

STATUS

approved

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Last modified January 23 22:36 EST 2020. Contains 331177 sequences. (Running on oeis4.)