OFFSET
0,33
FORMULA
T(n, k) =sum_j[T(n-k, j)] for k>j with T(0, 0)=1
EXAMPLE
Rows are {1,0,0,0,...}, {1,0,0,0,...}, {1,1,0,0,...}, {1,1,1,1,...}, {1,1,1,2,...} etc. T(7,4)=2 since 7 can be written as 4+3 or 4+2+1. T(12,6)=3 since 12 can be written as 6+5+1 or 6+4+2 or 6+3+2+1.
MATHEMATICA
t[n_?Positive, k_] := t[n, k] = Sum[t[n-k, j], {j, 0, k-1}]; t[0, 0] = 1; t[0, _] = 0; t[_?Negative, _] = 0; Table[ t[n, k], {n, 0, 13}, {k, 0, n}] // Flatten (* Jean-François Alcover, Sep 11 2012 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Henry Bottomley, Jan 30 2001
STATUS
approved