A280267 Square array read by rows: H_k(n,n), with rows n >= 0 and columns 0 <= k <= 3, where H_n is the n-th hyperoperation.

1, 0, 0, 1, 2, 2, 1, 1, 3, 4, 4, 4, 4, 6, 9, 27, 5, 8, 16, 256, 6, 10, 25, 3125, 7, 12, 36, 46656, 8, 14, 49, 823543, 9, 16, 64, 16777216, 10, 18, 81, 387420489, 11, 20, 100, 10000000000, 12, 22, 121, 285311670611, 13, 24, 144, 8916100448256, 14, 26, 169, 302875106592253

Offset: 0

Author

Natan Arie Consigli, Dec 30 2016

Keywords

• nonn
• tabf

Comments

See A054871 for definitions and key links.

The purpose of this sequence is to unify all the visible terms of the sequence a(k)= H_k(n,n) for some n.

Examples

			Square array begins:
1,  0,  0,   1;
2,  2,  1,   1;
3,  4,  4,   4;
4,  6,  9,   27;
5,  8,  16,  256;
6,  10, 25,  3125;
7,  12, 36,  46656;
8,  14, 49,  823543;
9,  16, 64,  16777216;
10, 18, 81,  387420489;
11, 20, 100, 10000000000;
12, 22, 121, 285311670611;
13, 24, 144, 8916100448256;
14, 26, 169, 302875106592253;
...
For line n=10 we have:
H_0(10,10) = 11.
H_1(10,10) = 20.
H_2(10,10) = 100.
H_3(10,10) = 10000000000.
		

Crossrefs

Cf. A054871, A280265 (table of H_k(n,2)).

Programs

Mathematica

H[0, x_, y_] := y + 1;
H[1, x_, y_] := x + y;
H[2, x_, y_] := x*y;
H[3, x_, y_] := x^y;
H[4, x_, 2] := x^x;
Table[H[k, n, n], {n, 0, 20}, {k, 0, 3}]