A265161 Array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = (3/2)*(3^k - 1) + A265159(n,k), n,k >= 1.

8, 35, 26, 89, 107, 80, 116, 269, 323, 242, 251, 350, 809, 971, 728, 278, 755, 1052, 2429, 2915, 2186, 332, 836, 2267, 3158, 7289, 8747, 6560, 359, 998, 2510, 6803, 9476, 21869, 26243, 19682, 737, 1079, 2996, 7532, 20411, 28430, 65609, 78731, 59048

Offset: 1

Author

L. Edson Jeffery, Dec 03 2015

Keywords

• nonn
• tabl

Comments

Conjecture 1: The array contains without duplication all possible "gap numbers" as defined in A265100.

Examples

			Array A begins:
.      8    26    80    242    728    2186    6560    19682    59048
.     35   107   323    971   2915    8747   26243    78731   236195
.     89   269   809   2429   7289   21869   65609   196829   590489
.    116   350  1052   3158   9476   28430   85292   255878   767636
.    251   755  2267   6803  20411   61235  183707   551123  1653371
.    278   836  2510   7532  22598   67796  203390   610172  1830518
.    332   998  2996   8990  26972   80918  242756   728270  2184812
.    359  1079  3239   9719  29159   87479  262439   787319  2361959
.    737  2213  6641  19925  59777  179333  538001  1614005  4842017
		

Crossrefs

Cf. A191107, A265100, A265104, A265159.

Programs

Mathematica

(* Array: *)
a005836[1] := 0; a005836[n_] := If[OddQ[n], 3*a005836[Floor[(n + 1)/2]], a005836[n - 1] + 1]; a265159[n_, k_] := 5 + 9*a005836[2^(k - 1)*(2 n - 1)]; a265161[n_, k_] := (3/2)*(3^k - 1) + a265159[n, k]; Grid[Table[a265161[n, k], {n, 9}, {k, 9}]]
(* Array antidiagonal flattened: *)
a005836[1] := 0; a005836[n_] := If[OddQ[n], 3*a005836[Floor[(n + 1)/2]], a005836[n - 1] + 1]; a265159[n_, k_] := 5 + 9*a005836[2^(k - 1)*(2 n - 1)]; a265161[n_, k_] := (3/2)*(3^k - 1) + a265159[n, k]; Flatten[Table[a265161[n - k + 1, k], {n, 9}, {k, n}]]

Formula

Conjecture 2: A(n,k) = A191107(n)*3^k - 1.