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

0,9

Links

Table of n, a(n) for n=0..27.

Eric Weisstein's World of Mathematics, Power Tower

Wikipedia, Knuth's up-arrow notation

Wikipedia, Tetration

Index entries for sequences related to tetration

Example

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,            ...
  ...

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);

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).

Sequence in context: A308211 A140130 A337087 * A327502 A354090 A362826

Adjacent sequences: A321309 A321310 A321311 * A321313 A321314 A321315

Keyword

nonn,tabl

Author

Alois P. Heinz, Nov 03 2018

Status

approved