OFFSET
0,19
LINKS
Alois P. Heinz, Antidiagonals n = 0..200, flattened
EXAMPLE
Square array A(n,k) begins:
0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 1, 1, 1, 1, 1, 1, 1, ...
0, 1, 2, 2, 2, 2, 2, 2, 2, ...
0, 2, 3, 4, 4, 4, 4, 4, 4, ...
0, 3, 7, 8, 9, 9, 9, 9, 9, ...
0, 6, 15, 18, 19, 20, 20, 20, 20, ...
0, 12, 34, 43, 46, 47, 48, 48, 48, ...
0, 25, 79, 102, 110, 113, 114, 115, 115, ...
MAPLE
h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),
`if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))
end:
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))
end:
A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):
seq(seq(A(n, d-n), n=0..d), d=0..14);
MATHEMATICA
h[n_, m_, t_, k_] := h[n, m, t, k] = If[m == 0, Binomial[n + t, t], If[n == 0, 0, Sum[h[n - 1, m - j, t + 1, k], {j, 1, Min[k, m]}]]];
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, i - 1, k]*h[A[i, k], j, 0, k], {j, 0, n/i}]]];
A[n_, k_] := If[n < 2, n, b[n - 1, n - 1, k]];
Table[A[n, d - n], {d, 0, 14}, {n, 0, d}] // Flatten (* Jean-François Alcover, May 11 2019, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 02 2018
STATUS
approved