A104385 Number of distinct partitions of triangular numbers n*(n+1)/2 into 3 parts for n>=1.

0, 0, 1, 4, 12, 27, 52, 91, 147, 225, 331, 469, 645, 867, 1141, 1474, 1875, 2352, 2914, 3571, 4332, 5208, 6211, 7351, 8640, 10092, 11719, 13534, 15552, 17787, 20254, 22969, 25947, 29205, 32761, 36631, 40833, 45387, 50311, 55624

Offset: 1

Author

Paul D. Hanna, Mar 04 2005

Keywords

• nonn

Comments

Equals the third column in triangle A104382.

Crossrefs

Cf. A000009, A104382.

Programs

PARI

{a(n)=if(n<1,0,polcoeff(polcoeff( prod(i=1,n*(n+1)/2,1+y*x^i,1+x*O(x^(n*(n+1)/2))),n*(n+1)/2,x),3,y))}

Formula

a(n) = round((3n^4 + 6n^3 - 33n^2 - 36n + 110)/144) (conjectured). - Ralf Stephan, Nov 13 2010.