A059881 As upper right triangle: wiggly sums to n where first term is k (sums in which terms alternately increase and decrease or vice versa; zigzag and zagzig partitions).

1, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 2, 1, 1, 1, 4, 4, 1, 1, 1, 1, 6, 5, 3, 2, 1, 1, 1, 9, 8, 5, 2, 2, 1, 1, 1, 14, 13, 9, 4, 3, 2, 1, 1, 1, 23, 19, 14, 8, 3, 3, 2, 1, 1, 1, 35, 31, 20, 13, 7, 4, 3, 2, 1, 1, 1, 55, 49, 32, 20, 12, 6, 4, 3, 2, 1, 1, 1, 87, 76, 50, 32, 18, 11, 7, 4, 3, 2, 1, 1, 1, 136

Offset: 1

Author

Henry Bottomley, Feb 05 2001

Keywords

• nonn
• tabl

Examples

			Rows start (1,0,1,2,2,...), (1,1,0,2,...), (1,1,1,...) etc. T(10,4)=8 since 10 can be written as 4+6, 4+5+1, 4+2+4, 4+2+3+1, 4+1+5, 4+1+4+1, 4+1+3+2, or 4+1+2+1+2.
		

Crossrefs

Column sums are A025047. Cf. A025048, A025049, A059882, A059883.

Formula

T(n, k) =A059882(n, k)+A059883(n, k) if n>k>0; T(n, n)=1 if n>0.