A066448 Triangle T(n,k) giving number of basis partitions of n with a Durfee square of order k (n >= 0, 0 <= k <= n).

1, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 2, 10, 1, 0, 0, 0, 0, 0, 0, 0, 2, 12, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 14, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 16, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

N. J. A. Sloane, Dec 29 2001

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  1;
  0, 1;
  0, 2, 0;
  0, 2, 0, 0;
  0, 2, 1, 0, 0;
  0, 2, 2, 0, 0, 0;
  0, 2, 4, 0, 0, 0, 0;
  0, 2, 6, 0, 0, 0, 0, 0;
  0, 2, 8, 0, 0, 0, 0, 0, 0;
  ...
		

Links

• Seiichi Manyama, Rows n = 0..139, flattened
• J. M. Nolan, C. D. Savage and H. S. Wilf, Basis partitions, Discrete Math. 179 (1998), 277-283.

Crossrefs

Row sums give A066447.

Programs

Maple

T := proc(n,d); option remember; if n=0 and d=0 then RETURN(1) elif n<=0 or d<=0 then RETURN(0) else RETURN(T(n-d,d)+T(n-2*d+1,d-1)+T(n-3*d+1,d-1)) fi:

PARI

T(n,k)=if(k<0||k>n,0,if(k==0,n==0,T(n-k,k)+T(n-2*k+1,k-1)+T(n-3*k+1,k-1))) /* Michael Somos, Mar 10 2004 */