OFFSET
0,7
LINKS
Alois P. Heinz, Rows n = 0..200, flattened
EXAMPLE
T(4,0) = 6: (1111,22), (1111,4), (211,4), (22,31), (22,4), (31,4).
T(4,1) = 4: (1111,31), (211,22), (211,31), (4,4).
T(4,2) = 3: (1111,211), (22,22), (31,31).
T(4,3) = 1: (211,211).
T(4,4) = 1: (1111,1111).
Triangle T(n,k) begins:
1;
0, 1;
1, 1, 1;
2, 2, 1, 1;
6, 4, 3, 1, 1;
8, 10, 5, 3, 1, 1;
24, 18, 13, 6, 3, 1, 1;
30, 42, 23, 14, 6, 3, 1, 1;
74, 72, 55, 26, 15, 6, 3, 1, 1;
110, 146, 95, 61, 27, 15, 6, 3, 1, 1;
219, 256, 201, 109, 64, 28, 15, 6, 3, 1, 1;
...
MAPLE
b:= proc(n, m, i) option remember; `if`(m=0, 1, `if`(i<1, 0,
add(add(expand(b(sort([n-i*j, m-i*h])[], i-1)*
x^min(j, h)), h=0..m/i), j=0..n/i)))
end:
g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(expand(g(n-i*j, i-1)*x^j), j=0..n/i)))
end:
T:= (n, k)-> (coeff(b(n$3), x, k)+coeff(g(n$2), x, k))/2:
seq(seq(T(n, k), k=0..n), n=0..12);
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Feb 11 2024
STATUS
approved