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%I #28 Apr 03 2024 03:38:25
%S 0,1,4,2,6,8,3,9,11,12,5,13,15,17,16,7,18,21,23,22,20,10,25,29,31,30,
%T 27,24,14,34,39,42,41,37,33,28,19,46,53,57,55,50,45,38,32,26,62,71,77,
%U 74,67,61,51,43,36,35,83,95,103,99,90,82,69,58,49,40
%N Table T(n, k) read by downward antidiagonals: T(n, k) = floor((4*T(n, k-1)+3)/3) starting with T(n, 0) = 4*n.
%C Permutation of nonnegative numbers.
%C Let b(m) be the row n in which m appears, this sequence would start: 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 1, 3,... . If we would remove in this sequence the first appearance of each number then we would obtain again the same sequence, hence b(m) is a fractal sequence. - _Thomas Scheuerle_, Dec 04 2023
%H Paolo Xausa, <a href="/A367882/b367882.txt">Table of n, a(n) for n = 0..11324</a> (first 150 antidiagonals, flattened).
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>
%F T(n, 0) = 4*n = A008586(n).
%F T(3*n, 1) = 16*n + 1 = A158057(n).
%F T(3*n+1, 1) = 16*n + 6 = 2*A017101(n).
%F T(3*n+2, 1) = 16*n + 11 = A106839(n).
%F T(3^k+n, k) = 4^(k+1) + T(n, k). - _Thomas Scheuerle_, Dec 04 2023
%e Square array starts:
%e 0, 1, 2, 3, 5, 7, ...
%e 4, 6, 9, 13, 18, 25, ...
%e 8, 11, 15, 21, 29, 39, ...
%e 12, 17, 23, 31, 42, 57, ...
%e 16, 22, 30, 41, 55, 74, ...
%e ...
%t A367882[n_, k_] := A367882[n, k] = If[k == 0, 4*n, Floor[4*A367882[n, k-1]/3 + 1]];
%t Table[A367882[k, n-k], {n, 0, 10}, {k, 0, n}] (* _Paolo Xausa_, Apr 03 2024 *)
%o (PARI) T(n, k) = if(k==0, 4*n, (4*T(n, k-1)+3)\3) \\ _Thomas Scheuerle_, Dec 04 2023
%Y Cf. A008586, A017101, A106839, A158057.
%K nonn,tabl
%O 0,3
%A _Philippe Deléham_, Dec 04 2023
%E More terms from _Paolo Xausa_, Apr 03 2024
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