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
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.
Programs
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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}]
Comments