OFFSET
1,6
LINKS
Alois P. Heinz, Antidiagonals n = 1..65, flattened
N. J. A. Sloane, Transforms
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, ...
2, 4, 8, 16, 32, ...
4, 16, 64, 256, 1024, ...
9, 70, 540, 4216, 33264, ...
MAPLE
with(numtheory): dc:= proc(b, c) proc(n) option remember; add(b(d) *c(n/d), d=`if`(n<0, {}, divisors(n))) end end: A:= proc(n, k) local a, b, t; b[1]:= dc(a, a); for t from 2 to k do b[t]:= dc(b[t-1], b[t-1]) od: a:= n-> `if`(n=1, 1, b[k](n-1)); a(n) end: seq(seq(A(n, 1+d-n), n=1..d), d=1..11);
MATHEMATICA
dc[b_, c_] := Module[{proc}, proc[n_] := proc[n] = Sum [b[d] *c[n/d], {d, If[n < 0, {}, Divisors[n]]}]; proc]; A [n_, k_] := Module[{a, b, t}, b[1] = dc[a, a]; For[t = 2, t <= k, t++, b[t] = dc[b[t-1], b[t-1]]]; a = Function[m, If[m == 1, 1, b[k][m-1]]]; a[n]]; Table[Table[A[n, 1+d-n], {n, 1, d}], {d, 1, 11}] // Flatten (* Jean-François Alcover, Dec 20 2013, translated from Maple *)
CROSSREFS
KEYWORD
AUTHOR
Alois P. Heinz, Sep 17 2008
STATUS
approved