A059882 As upper right triangle: ascending wiggly sums to n where first term is k (sums in which terms alternately increase and decrease; zigzag partitions).

1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 2, 1, 0, 0, 1, 4, 2, 0, 0, 0, 1, 6, 3, 1, 0, 0, 0, 1, 9, 4, 2, 0, 0, 0, 0, 1, 14, 7, 3, 1, 0, 0, 0, 0, 1, 23, 10, 5, 2, 0, 0, 0, 0, 0, 1, 35, 17, 7, 3, 1, 0, 0, 0, 0, 0, 1, 55, 26, 11, 5, 2, 0, 0, 0, 0, 0, 0, 1, 87, 41, 17, 8, 3, 1, 0, 0, 0, 0, 0, 0, 1, 136, 64, 28, 11, 5, 2

Offset: 1

Author

Henry Bottomley, Feb 05 2001

Keywords

• nonn
• tabl

Examples

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

Crossrefs

Column sums are A025048. Cf. A025047, A025049, A059881, A059883.

Formula

If n>k>0 T(n, k)=sum_j[S(n-k, j)] over j>k and if n>0 T(n, n)=1; where S(n, k)=A059883(n, k) and if n>k>0, S(n, k)=sum_j[T(n-k, j)] over k>j (note reversal) and if n>0 S(n, n)=1.