OFFSET
0,8
LINKS
Alois P. Heinz, Rows n = 0..200, flattened
Wikipedia, Triangular number
EXAMPLE
Triangle T(n,k) begins:
1;
1, 1;
1, 1, 1;
1, 2, 1, 1;
1, 2, 2, 1, 1;
1, 2, 3, 3, 1, 1;
1, 3, 4, 5, 3, 1, 1;
1, 3, 5, 8, 6, 4, 1, 1;
1, 3, 7, 12, 11, 9, 4, 1, 1;
1, 3, 9, 16, 20, 18, 11, 5, 1, 1;
1, 4, 10, 22, 32, 35, 26, 14, 5, 1, 1;
1, 4, 12, 29, 48, 61, 55, 36, 17, 6, 1, 1;
1, 4, 14, 37, 70, 100, 106, 84, 48, 21, 6, 1, 1;
MAPLE
b:= proc(n, s) option remember; expand(`if`(n=0,
`if`(issqr(8*s+1), 1, 0), b(n-1, s)+x*b(n-1, s+n)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b(n, 0)):
seq(T(n), n=0..16);
MATHEMATICA
b[n_, s_] := b[n, s] = Expand[If[n == 0, If[IntegerQ @ Sqrt[8*s + 1], 1, 0], b[n - 1, s] + x*b[n - 1, s + n]]];
T[n_] := Function [p, Table[Coefficient[p, x, i], {i, 0, n}]][b[n, 0]];
Table[T[n], {n, 0, 16}] // Flatten (*Jean-François Alcover, May 29 2018, from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Mar 23 2017
STATUS
approved