A059883 As upper right triangle: descending wiggly sums to n where first term is k (sums in which terms alternately decrease and increase; zagzig partitions).

1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 2, 2, 1, 1, 1, 0, 4, 3, 2, 2, 1, 1, 1, 0, 6, 6, 3, 3, 2, 1, 1, 1, 0, 9, 9, 6, 3, 3, 2, 1, 1, 1, 0, 14, 13, 10, 6, 4, 3, 2, 1, 1, 1, 0, 23, 21, 15, 10, 6, 4, 3, 2, 1, 1, 1, 0, 35, 33, 24, 15, 10, 7, 4, 3, 2, 1, 1, 1, 0, 55, 52, 38, 25, 15, 10, 7, 4, 3, 2, 1, 1, 1

Offset: 1

Author

Henry Bottomley, Feb 05 2001

Keywords

• nonn
• tabl

Examples

			Rows start (1,0,0,0,0,...), (1,1,0,1,...), (1,1,1,...) etc. T(10,4)=6 since 10 can be written as 4+2+4, 4+2+3+1, 4+1+5, 4+1+4+1, 4+1+3+2, or 4+1+2+1+2.
		

Links

• Alois P. Heinz, Rows n = 1..200, flattened

Crossrefs

Column sums are A025049. Cf. A025047, A025048, A059881, A059882.

Formula

If n>k>0 T(n, k)=sum_j[S(n-k, j)] over k>j and if n>0 T(n, n)=1; where S(n, k)=A059882(n, k) and if n>k>0, S(n, k)=sum_j[T(n-k, j)] over j>k (note reversal) and if n>0 S(n, n)=1.