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

1,7

Links

Table of n, a(n) for n=1..92.

Formula

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

Example

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.

Sequence in context: A118198 A348691 A290885 * A096568 A025862 A004540

Adjacent sequences: A059878 A059879 A059880 * A059882 A059883 A059884

Keyword

nonn,tabl

Author

Henry Bottomley, Feb 05 2001

Status

approved