A367882 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.

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, 27, 24, 14, 34, 39, 42, 41, 37, 33, 28, 19, 46, 53, 57, 55, 50, 45, 38, 32, 26, 62, 71, 77, 74, 67, 61, 51, 43, 36, 35, 83, 95, 103, 99, 90, 82, 69, 58, 49, 40

Offset: 0

Author

Philippe Deléham, Dec 04 2023

Keywords

• nonn
• tabl

Comments

Permutation of nonnegative numbers.

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

Examples

			Square array starts:
  0,   1,   2,   3,   5,   7, ...
  4,   6,   9,  13,  18,  25, ...
  8,  11,  15,  21,  29,  39, ...
 12,  17,  23,  31,  42,  57, ...
 16,  22,  30,  41,  55,  74, ...
 ...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..11324 (first 150 antidiagonals, flattened).
• Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

Cf. A008586, A017101, A106839, A158057.

Programs

Mathematica

A367882[n_, k_] := A367882[n, k] = If[k == 0, 4*n, Floor[4*A367882[n, k-1]/3 + 1]];
Table[A367882[k, n-k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Apr 03 2024 *)

PARI

T(n, k) = if(k==0, 4*n, (4*T(n, k-1)+3)\3) \\ Thomas Scheuerle, Dec 04 2023

Formula

T(n, 0) = 4*n = A008586(n).

T(3*n, 1) = 16*n + 1 = A158057(n).

T(3*n+1, 1) = 16*n + 6 = 2*A017101(n).

T(3*n+2, 1) = 16*n + 11 = A106839(n).

T(3^k+n, k) = 4^(k+1) + T(n, k). - Thomas Scheuerle, Dec 04 2023

Extensions

More terms from Paolo Xausa, Apr 03 2024