OFFSET
1,4
COMMENTS
Weakly unimodal means nondecreasing then nonincreasing.
FORMULA
T(n, k) = S(n, k) - S(n-k, k) + Sum_j[T(n-k, j)] for j >= k, where S(n, k) = A008284(n, k) = Sum_j[S(n-k, j)] for n>k >= j [note reversal] with S[n, n] = 1.
EXAMPLE
Rows are {1,1,2,4,8,15,...}, {1,1,2,3,5,8,...}, {1,1,2,3,5,7,...} etc.
As an upper right triangle:
1, 1, 2, 4, 8, 15, ...,
1, 1, 2, 3, 5, 8, ...,
1, 1, 2, 3, 5, 7, ...,
...
As a left downward triangle, it starts:
1;
1, 1;
2, 1, 1;
4, 2, 1, 1;
8, 3, 2, 1, 1;
15, 5, 3, 2, 1, 1;
27, 8, 5, 3, 2, 1, 1;
...
T(9,3)=11 since 9 can be written as 3+6, 3+5+1, 3+4+2, 3+4+1+1, 3+3+3, 3+3+2+1, 3+3+1+1+1, 3+2+2+2, 3+2+2+1+1, 3+2+1+1+1+1 or 3+1+1+1+1+1.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Henry Bottomley, Feb 01 2001
STATUS
approved