A059883 - OEIS

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

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OFFSET

1,17

LINKS

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

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.

EXAMPLE

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.

CROSSREFS

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

Sequence in context: A353329 A282778 A342788 * A086967 A098490 A247138

Adjacent sequences: A059880 A059881 A059882 * A059884 A059885 A059886

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Feb 05 2001

STATUS

approved