OFFSET
1,1
COMMENTS
Same as A028657 without first row and column.
LINKS
Alois P. Heinz, Antidiagonals m = 1..45, flattened
Adalbert Kerber, Applied Finite Group Actions, second edition, Springer-Verlag, (1999). See table under Corollary 2.3.1 on page 68.
EXAMPLE
The array begins:
2 3 4 5 6 7 8 9 ...
3 7 13 22 34 50 70 95 ...
4 13 36 87 190 386 734 1324 ...
5 22 87 317 1053 3250 9343 25207 ...
6 34 190 1053 5624 28576 136758 613894 ...
7 50 386 3250 28576 251610 2141733 17256831 ...
8 70 734 9343 136758 2141733 33642660 508147108 ...
9 95 1324 25207 613894 17256831 508147108 14685630688 ...
(cf. A028657).
MAPLE
b:= proc(n, i) b(n, i):= `if`(n=0, [[]], `if`(i<1, [], [seq(map(
p->`if`(j=0, p, [p[], [i, j]]), b(n-i*j, i-1))[], j=0..n/i)]))
end:
g:= proc(n, k) option remember; add(add(2^add(add(i[2]*j[2]*
igcd(i[1], j[1]), j=t), i=s) /mul(i[1]^i[2]*i[2]!, i=s)
/mul(i[1]^i[2]*i[2]!, i=t), t=b(n+k$2)), s=b(n$2))
end:
A:= (m, n)-> g(min(m, n), abs(m-n)):
seq(seq(A(m, 1+d-m), m=1..d), d=1..12); # Alois P. Heinz, Aug 13 2014
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, {0}, If[i < 1, {}, Union[Flatten[Table[ Function[{p}, p + j*x^i] /@ b[n - i*j, i - 1], {j, 0, n/i}]]]]];
g[n_, k_] := g[n, k] = Sum[Sum[2^Sum[Sum[GCD[i, j]*Coefficient[s, x, i]* Coefficient[t, x, j], {j, 1, Exponent[t, x]}], {i, 1, Exponent[s, x]}]/ Product[i^Coefficient[s, x, i]*Coefficient[s, x, i]!, {i, 1, Exponent[s, x]}]/Product[i^Coefficient[t, x, i]*Coefficient[t, x, i]!, {i, 1, Exponent[t, x]}], {t, b[n + k, n + k]}], {s, b[n, n]}];
A[n_, k_] := g[Min[n, k], Abs[n - k]];
Table[A[n - k + 1, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 09 2019, after Alois P. Heinz in A028657 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Don Knuth, Aug 09 2014
STATUS
approved