OFFSET
0,6
LINKS
Alois P. Heinz, Rows n = 0..50, flattened
EXAMPLE
Triangle T(n,k) begins:
1;
1;
1, 1;
1, 2, 1;
1, 3, 3, 2, 2, 0, 1;
1, 4, 6, 6, 6, 3, 4, 2, 1, 1;
1, 5, 10, 13, 15, 12, 14, 15, 9, 12, 5, 5, 1, 1;
1, 6, 15, 24, 32, 33, 37, 46, 40, 43, 34, 28, 23, 16, 10, 5, 2, 1;
MAPLE
b:= proc(x, y) option remember; `if`(y<0 or x<y, 0, `if`(x=0, 1,
expand(add(z^(y+j/2)*b(x-1, y+j), j=[-1, -3, 0, 1, 3]))))
end:
T:= n-> (p->seq(coeff(p, z, i), i=0..degree(p)))(b(n, 0)):
seq(T(n), n=0..10);
MATHEMATICA
b[x_, y_] := b[x, y] = If[y < 0 || x < y, 0, If[x == 0, 1,
Expand[Sum[z^(y+j/2)*b[x-1, y+j], {j, {-1, -3, 0, 1, 3}}]]]];
T[n_] := CoefficientList[b[n, 0], z];
Table[T[n], {n, 0, 10}] // Flatten (* Jean-François Alcover, Apr 29 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Sep 23 2014
STATUS
approved