A367856 - OEIS

%I #22 Apr 03 2024 03:38:21

%S 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,

%T 23,18,26,47,58,52,44,35,28,21,40,71,88,79,67,53,43,32,24,61,107,133,

%U 119,101,80,65,49,37,27,92,161,200,179,152,121,98,74,56,41,30

%N 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.

%C Permutation of nonnegative numbers.

%H Paolo Xausa, <a href="/A367856/b367856.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 natural numbers</a>.

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

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

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

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

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

%e Square array starts:

%e   0,  1,  2,  4,   7,  11,  17,  26,  40,   61, ...

%e   3,  5,  8, 13,  20,  31,  47,  71, 107,  161, ...

%e   6, 10, 16, 25,  38,  58,  88, 133, 200,  301, ...

%e   9, 14, 22, 34,  52,  79, 119, 179, 269,  404, ...

%e  12, 19, 29, 44,  67, 101, 152, 229, 344,  517, ...

%e  15, 23, 35, 53,  80, 121, 182, 274, 412,  619, ...

%e  18, 28, 43, 65,  98, 148, 223, 335, 503,  755, ...

%e  21, 32, 49, 74, 112, 169, 254, 382, 574,  862, ...

%e  24, 37, 56, 85, 128, 193, 290, 436, 655,  983, ...

%e  27, 41, 62, 94, 142, 214, 322, 484, 727, 1091, ...

%e  ...

%t A367856[n_, k_] := A367856[n, k] = If[k == 0, 3*n, Floor[3*A367856[n, k-1]/2 + 1]];

%t Table[A367856[k, n-k], {n, 0, 10}, {k, 0, n}] (* _Paolo Xausa_, Apr 03 2024 *)

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

%K nonn,tabl

%O 0,3

%A _Philippe Deléham_, Dec 03 2023

%E More terms from _Paolo Xausa_, Apr 03 2024