A367856 Table T(n,k), read by downward antidiagonals: T(n,k) = floor((3*T(n,k-1)+2)/2) starting with T(n,0) = 3*n.

0, 1, 3, 2, 5, 6, 4, 8, 10, 9, 7, 13, 16, 14, 12, 11, 20, 25, 22, 19, 15, 17, 31, 38, 34, 29, 23, 18, 26, 47, 58, 52, 44, 35, 28, 21, 40, 71, 88, 79, 67, 53, 43, 32, 24, 61, 107, 133, 119, 101, 80, 65, 49, 37, 27, 92, 161, 200, 179, 152, 121, 98, 74, 56, 41, 30

Offset: 0

Author

Philippe Deléham, Dec 03 2023

Keywords

• nonn
• tabl

Comments

Permutation of nonnegative numbers.

Examples

			Square array starts:
  0,  1,  2,  4,   7,  11,  17,  26,  40,   61, ...
  3,  5,  8, 13,  20,  31,  47,  71, 107,  161, ...
  6, 10, 16, 25,  38,  58,  88, 133, 200,  301, ...
  9, 14, 22, 34,  52,  79, 119, 179, 269,  404, ...
 12, 19, 29, 44,  67, 101, 152, 229, 344,  517, ...
 15, 23, 35, 53,  80, 121, 182, 274, 412,  619, ...
 18, 28, 43, 65,  98, 148, 223, 335, 503,  755, ...
 21, 32, 49, 74, 112, 169, 254, 382, 574,  862, ...
 24, 37, 56, 85, 128, 193, 290, 436, 655,  983, ...
 27, 41, 62, 94, 142, 214, 322, 484, 727, 1091, ...
 ...
		

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 natural numbers.

Crossrefs

Cf. A001651, A006999, A008585, A017173, A017221.

Programs

Mathematica

A367856[n_, k_] := A367856[n, k] = If[k == 0, 3*n, Floor[3*A367856[n, k-1]/2 + 1]];
Table[A367856[k, n-k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Apr 03 2024 *)

Formula

T(n,0) = 3*n = A008585(n).

T(2*n,1) = 9*n+1 = A017173(n).

T(2*n+1,1) = 9*n+5 = A017221(n).

T(0,k) = A006999(k).

T(2^k+n, k) = 3^(k+1) + T(n, k).

Extensions

More terms from Paolo Xausa, Apr 03 2024