OFFSET
0,6
COMMENTS
An isoscent sequence of length n is an integer sequence [s(1),...,s(n)] with s(1) = 0 and 0 <= s(i) <= 1 plus the number of level steps in [s(1),...,s(i)].
Columns k=0-10 give: A000012, A000295, A243228, A243229, A243230, A243231, A243232, A243233, A243234, A243235, A243236.
Row sums give A000110.
Last elements of rows give A243237.
LINKS
Joerg Arndt and Alois P. Heinz, Rows n = 0..100, flattened
EXAMPLE
T(4,0) = 1: [0,0,0,0].
T(4,1) = 11: [0,0,0,1], [0,0,0,2], [0,0,0,3], [0,0,1,0], [0,0,1,1], [0,0,2,0], [0,0,2,1], [0,0,2,2], [0,1,0,0], [0,1,1,0], [0,1,1,1].
T(4,2) = 3: [0,0,1,2], [0,1,0,1], [0,1,1,2].
Triangle T(n,k) begins:
1;
1;
1, 1;
1, 4;
1, 11, 3;
1, 26, 25;
1, 57, 128, 17;
1, 120, 525, 229, 2;
1, 247, 1901, 1819, 172;
1, 502, 6371, 11172, 3048, 53;
1, 1013, 20291, 58847, 33065, 2751, 7;
...
MAPLE
b:= proc(n, i, t) option remember; `if`(n<1, 1, expand(add(
`if`(j>i, x, 1) *b(n-1, j, t+`if`(j=i, 1, 0)), j=0..t+1)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n-1, 0$2)):
seq(T(n), n=0..15);
MATHEMATICA
b[n_, i_, t_] := b[n, i, t] = If[n<1, 1, Expand[Sum[If[j>i, x, 1]*b[n-1, j, t + If[j == i, 1, 0]], {j, 0, t+1}]]]; T[n_] := Function[{p}, Table[ Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][b[n-1, 0, 0]]; Table[T[n], {n, 0, 15}] // Flatten (* Jean-François Alcover, Feb 09 2015, after Maple *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Joerg Arndt and Alois P. Heinz, May 11 2014
STATUS
approved