A059776 Three-quadrant Ferrers graphs that partition n.

1, 2, 5, 11, 24, 48, 95, 178, 328, 585, 1025, 1754, 2958, 4897, 8002, 12889, 20523, 32289, 50296, 77550, 118521, 179553, 269881, 402532, 596178, 876942, 1281777, 1862015, 2689405, 3862891, 5519403, 7846393, 11100970, 15632733, 21917280

Offset: 0

Author

N. J. A. Sloane, Feb 21 2001

Keywords

• nonn
• easy

References

• G. E. Andrews, Three-quadrant Ferrers graphs, Indian J. Math., 42 (No. 1, 2000), 1-7.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000041, A001522, A059777.

Programs

Maple

t1 := add( (-1)^(j)*q^(j*(j+1)/2)*(1-q^(j+1))/(1-q),j=0..101); t3 := mul((1-q^n)^3,n=1..101); series(t1/t3,q,101);

Mathematica

nmax = 50; CoefficientList[Series[Sum[(-1)^k*x^(k*(k+1)/2)*(1 - x^(k + 1))/(1 - x), {k, 0, nmax}]/Product[(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 11 2018 *)

Formula

a(n) ~ exp(Pi*sqrt(2*n)) / (2^(11/2) * n^(3/2)). - Vaclav Kotesovec, Jul 12 2018