OFFSET
1,5
FORMULA
T(n, k) = number of paths from (0, 0) to (n-k, k) in directed graph having vertices (i, j) and edges (i, j)-to-(i+1, j) and (i, j)-to-(i, j+1) for i, j >= 0 and edges (i, j)-to-(i+1, j+1) for i odd and j >= i and for j odd and i >= j.
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 4, 8, 4, 1;
1, 5, 15, 15, 5, 1;
...
MATHEMATICA
T[_, 0] = 1; T[n_, n_] = 1; T[n_, k_] /; EvenQ[k] && 1 <= k/2 <= Floor[n/4] || EvenQ[n-k] && 1 <= (n-k)/2 <= Floor[n/4] := T[n, k] = T[n-1, k-1] + T[n-2, k-1] + T[n-1, k]; T[n_, k_] := T[n, k] = T[n-1, k-1] + T[n-1, k];
Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 02 2017 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved