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A280265 Array with five columns read by rows: H_k(n,2), with rows n >= 0 and columns 0 <= k <= 4, where H_n is the n-th hyperoperation.

%I A280265 #29 Jan 11 2020 15:57:47
%S A280265 3,2,0,1,1,3,3,2,1,1,3,4,4,4,4,3,5,6,9,27,3,6,8,16,256,3,7,10,25,3125,
%T A280265 3,8,12,36,46656,3,9,14,49,823543,3,10,16,64,16777216,3,11,18,81,
%U A280265 387420489,3,12,20,100,10000000000,3,13,22,121,285311670611,3,14,24,144,8916100448256
%N A280265 Array with five columns read by rows: H_k(n,2), with rows n >= 0 and columns 0 <= k <= 4, where H_n is the n-th hyperoperation.
%C A280265 See A054871 for definitions and key links.
%C A280265 The purpose of this sequence is to unify all the visible terms of the sequence:  a(k)= H_k(n,2) for some n.
%e A280265 Square array begins:
%e A280265 3, 2,  0,  1,   1;
%e A280265 3, 3,  2,  1,   1;
%e A280265 3, 4,  4,  4,   4;
%e A280265 3, 5,  6,  9,   27;
%e A280265 3, 6,  8,  16,  256;
%e A280265 3, 7,  10, 25,  3125;
%e A280265 3, 8,  12, 36,  46656;
%e A280265 3, 9,  14, 49,  823543;
%e A280265 3, 10, 16, 64,  16777216;
%e A280265 3, 11, 18, 81,  387420489;
%e A280265 3, 12, 20, 100, 10000000000;
%e A280265 3, 13, 22, 121, 285311670611;
%e A280265 3, 14, 24, 144, 8916100448256;
%e A280265 ...
%e A280265 For row 10 we have:
%e A280265 H_0(10,2) = 3;
%e A280265 H_1(10,2) = 12;
%e A280265 H_2(10,2) = 20;
%e A280265 H_3(10,2) = 100;
%e A280265 H_4(10,2) = 10000000000;
%t A280265 H[0, x_, y_] := y + 1;
%t A280265 H[1, x_, y_] := x + y;
%t A280265 H[2, x_, y_] := x*y;
%t A280265 H[3, x_, y_] := x^y;
%t A280265 H[4, x_, 2] := x^x;
%t A280265 Table[H[k, n, 2], {n, 0, 20}, {k, 0, 4}]
%Y A280265 Cf. A054871, A256131 (contains only line n=10), A280267, A000312.
%K A280265 nonn,tabf,easy
%O A280265 0,1
%A A280265 _Natan Arie Consigli_, Dec 30 2016
%E A280265 Definition corrected by _Natan Arie Consigli_, Jun 13 2017