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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).
4
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
1,7
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.
EXAMPLE
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.
Sequence in context: A324044 A364046 A001899 * A303206 A094247 A053694
KEYWORD
nonn,tabl
AUTHOR
Henry Bottomley, Feb 05 2001
STATUS
approved