login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Three-quadrant Ferrers graphs that partition n.
3

%I #8 Jul 12 2018 02:46:56

%S 1,2,5,11,24,48,95,178,328,585,1025,1754,2958,4897,8002,12889,20523,

%T 32289,50296,77550,118521,179553,269881,402532,596178,876942,1281777,

%U 1862015,2689405,3862891,5519403,7846393,11100970,15632733,21917280

%N Three-quadrant Ferrers graphs that partition n.

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

%H Vaclav Kotesovec, <a href="/A059776/b059776.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(Pi*sqrt(2*n)) / (2^(11/2) * n^(3/2)). - _Vaclav Kotesovec_, Jul 12 2018

%p 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);

%t 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 *)

%Y Cf. A000041, A001522, A059777.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Feb 21 2001