OFFSET
0,12
LINKS
Alois P. Heinz, Rows n = 0..400, flattened
EXAMPLE
T(8,3) = 5: [6,1,1], [5,2,1], [4,3,1], [4,2,2], [3,3,2].
T(8,4) = 3: [4,2,1,1], [3,3,1,1], [3,2,2,1].
T(9,3) = 6: [7,1,1], [6,2,1], [5,3,1], [4,4,1], [5,2,2], [4,3,2].
T(9,4) = 4: [5,2,1,1], [4,3,1,1], [4,2,2,1], [3,3,2,1].
T(9,5) = 1: [3,2,2,1,1].
Triangle begins:
1;
0, 1;
0, 1, 1;
0, 1, 1;
0, 1, 2, 1;
0, 1, 2, 2;
0, 1, 3, 2, 1;
0, 1, 3, 4, 1;
0, 1, 4, 5, 3;
0, 1, 4, 6, 4, 1;
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(expand(b(n-i*j, i-1)*x^j), j=0..min(2, n/i))))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n$2)):
seq(T(n), n=0..20);
MATHEMATICA
max = 15; g = -1+Product[1+t*x^j+t^2*x^(2j), {j, 1, max}]; t[n_, k_] := SeriesCoefficient[g, {x, 0, n}, {t, 0, k}]; t[0, 0] = 1; Table[Table[t[n, k], {k, 0, n}] /. {a__, 0 ..} -> {a}, {n, 0, max}] // Flatten (* Jean-François Alcover, Jan 08 2014 *)
CROSSREFS
KEYWORD
AUTHOR
Alois P. Heinz, Jan 19 2013
STATUS
approved