A321312 A(n,k) = n^^k is the k-th tetration of n; square array A(n,k), n>=0, k>=0, read by antidiagonals.

1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 4, 3, 1, 0, 1, 16, 27, 4, 1, 1, 1, 65536, 7625597484987, 256, 5, 1

Offset: 0

Author

Alois P. Heinz, Nov 03 2018

Keywords

• nonn
• tabl

Examples

			Square array A(n,k) begins:
  1, 0,      1,              0,      1,   0,   1, ...
  1, 1,      1,              1,      1,   1,   1, ...
  1, 2,      4,             16,  65536, ...
  1, 3,     27,  7625597484987,    ...
  1, 4,    256,            ...
  1, 5,   3125,            ...
  1, 6,  46656,            ...
  1, 7, 823543,            ...
  ...
		

Links

• Eric Weisstein's World of Mathematics, Power Tower
• Wikipedia, Knuth's up-arrow notation
• Wikipedia, Tetration
• Index entries for sequences related to tetration

Crossrefs

Columns k=0-3 give: A000012, A001477, A000312, A002488.

Rows n=0-4 give: A059841, A000012, A014221, A014222(k+1), A114561(k+1).

Main diagonal gives A004231 (Ackermann's sequence).

Cf. A027747, A171882 (by upwards diagonals).

Programs

Maple

A:= (n, k)-> `if`(k=0, 1, n^A(n, k-1)):
seq(seq(A(n, d-n), n=0..d), d=0..6);