cp's OEIS Frontend

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.

%I A280267 #12 Jan 11 2020 15:57:47
%S A280267 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,
%T A280267 46656,8,14,49,823543,9,16,64,16777216,10,18,81,387420489,11,20,100,
%U A280267 10000000000,12,22,121,285311670611,13,24,144,8916100448256,14,26,169,302875106592253
%N 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.
%C A280267 See A054871 for definitions and key links.
%C A280267 The purpose of this sequence is to unify all the visible terms of the sequence a(k)= H_k(n,n) for some n.
%e A280267 Square array begins:
%e A280267 1,  0,  0,   1;
%e A280267 2,  2,  1,   1;
%e A280267 3,  4,  4,   4;
%e A280267 4,  6,  9,   27;
%e A280267 5,  8,  16,  256;
%e A280267 6,  10, 25,  3125;
%e A280267 7,  12, 36,  46656;
%e A280267 8,  14, 49,  823543;
%e A280267 9,  16, 64,  16777216;
%e A280267 10, 18, 81,  387420489;
%e A280267 11, 20, 100, 10000000000;
%e A280267 12, 22, 121, 285311670611;
%e A280267 13, 24, 144, 8916100448256;
%e A280267 14, 26, 169, 302875106592253;
%e A280267 ...
%e A280267 For line n=10 we have:
%e A280267 H_0(10,10) = 11.
%e A280267 H_1(10,10) = 20.
%e A280267 H_2(10,10) = 100.
%e A280267 H_3(10,10) = 10000000000.
%t A280267 H[0, x_, y_] := y + 1;
%t A280267 H[1, x_, y_] := x + y;
%t A280267 H[2, x_, y_] := x*y;
%t A280267 H[3, x_, y_] := x^y;
%t A280267 H[4, x_, 2] := x^x;
%t A280267 Table[H[k, n, n], {n, 0, 20}, {k, 0, 3}]
%Y A280267 Cf. A054871, A280265 (table of H_k(n,2)).
%K A280267 nonn,tabf
%O A280267 0,5
%A A280267 _Natan Arie Consigli_, Dec 30 2016