OFFSET
0,5
COMMENTS
LINKS
Alois P. Heinz, Rows n = 0..18, flattened
EXAMPLE
T(3,1) = 10: [1,1,1], [2,1,1], [2,2,1], [2,2,2], [3,1,1], [3,2,1], [3,2,2], [3,3,1], [3,3,2], [3,3,3].
T(3,3) = 1: [1,2,3].
Triangle T(n,k) begins:
1;
0, 1;
0, 3, 1;
0, 10, 16, 1;
0, 35, 175, 45, 1;
0, 126, 1771, 1131, 96, 1;
0, 462, 17906, 23611, 4501, 175, 1;
0, 1716, 184920, 461154, 161876, 13588, 288, 1;
...
MAPLE
b:= proc(n, l) option remember; `if`(n=0, 1, add(b(n-1, [seq(min(l[j],
`if`(j=1 or l[j-1]<i, i, l[j])), j=1..nops(l))]), i=1..l[-1]))
end:
A:= (n, k)-> `if`(k=0, `if`(n=0, 1, 0), b(n, [n$k])):
T:= (n, k)-> A(n, k) -`if`(k=0, 0, A(n, k-1)):
seq(seq(T(n, k), k=0..n), n=0..9);
MATHEMATICA
b[n_, l_List] := b[n, l] = If[n == 0, 1, Sum[b[n-1, Table[Min[l[[j]], If[j == 1 || l[[j-1]]<i, i, l[[j]]]], {j, 1, Length[l]}]], {i, 1, l[[-1]]}]]; A[n_, k_] := If[k == 0, If[n == 0, 1, 0], b[n, Array[n&, k]]]; T[n_, k_] := A[n, k] - If[k == 0, 0, A[n, k-1]]; Table[Table[T[n, k], {k, 0, n}], {n, 0, 9}] // Flatten (* Jean-François Alcover, Feb 04 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Jul 28 2014
STATUS
approved