OFFSET
0,3
COMMENTS
Row sums are 0, 0, 3, 5, 15, 26, 59, 101, 207, 350, 680,...
The first column is essentially A000045, and the other columns also join the Fibonacci sequence after some transient initial terms.
EXAMPLE
0;
0;
2, 1, 0;
3, 2, 0;
5, 5, 4, 1, 0;
8, 8, 7, 3, 0;
13, 13, 13, 12, 7, 1, 0;
21, 21, 21, 20, 14, 4, 0;
34, 34, 34, 34, 33, 26, 11, 1, 0;
55, 55, 55, 55, 54, 46, 25, 5, 0;
89, 89, 89, 89, 89, 88, 79, 51, 16, 1, 0;
MATHEMATICA
w[n_, m_, k_] = Binomial[n - (m + k), m + k];
t[n_, k_] := Sum[w[n, m, k], {m, 1, Floor[n/2 - k]}];
Table[Table[t[n, k], {k, -Floor[n/2], Floor[n/2]}], {n, 0, 10}];
Flatten[%]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Roger L. Bagula, Dec 10 2010
STATUS
approved