OFFSET
0,3
LINKS
Alois P. Heinz, Rows n = 0..150, flattened
EXAMPLE
T(4,0) = 7: [4], [3,1], [2,2], [1,3], [2,1,1], [1,2,1], [1,1,2].
T(7,1) = 11: [4,1,1,1], [2,2,2,1], [1,2,2,2], [1,1,1,4], [1,3,1,1,1], [2,2,1,1,1], [1,1,1,3,1], [2,1,1,1,2], [1,1,1,2,2], [1,1,1,2,1,1], [1,1,2,1,1,1].
T(7,2) = 4: [3,1,1,1,1], [1,1,1,1,3], [1,2,1,1,1,1], [1,1,1,1,2,1].
T(7,3) = 2: [2,1,1,1,1,1], [1,1,1,1,1,2].
T(7,5) = 1: [1,1,1,1,1,1,1].
Triangle T(n,k) begins:
: 0 : 1;
: 1 : 1;
: 2 : 2;
: 3 : 3, 1;
: 4 : 7, 0, 1;
: 5 : 13, 2, 0, 1;
: 6 : 24, 5, 2, 0, 1;
: 7 : 46, 11, 4, 2, 0, 1;
: 8 : 89, 21, 11, 4, 2, 0, 1;
: 9 : 170, 45, 23, 11, 4, 2, 0, 1;
: 10 : 324, 99, 47, 23, 12, 4, 2, 0, 1;
MAPLE
b:= proc(n, t) option remember; `if`(n=0, 1,
expand(add(`if`(abs(t)<>j, b(n-j, j),
`if`(t<0, x, 1)*b(n-j, -j)), j=1..n)))
end:
T:= n->(p->seq(coeff(p, x, i), i=0..degree(p)))(b(n, 0)):
seq(T(n), n=0..15);
MATHEMATICA
b[n_, t_] := b[n, t] = If[n==0, 1, Expand[Sum[If[Abs[t] != j, b[n-j, j], If[t<0, x, 1]*b[n-j, -j]], {j, 1, n}]]]; T[n_] := Function[p, Table[ Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][b[n, 0]]; Table[T[n], {n, 0, 15}] // Flatten (* Jean-François Alcover, Feb 08 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Nov 23 2013
STATUS
approved