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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..45.

FORMULA

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

EXAMPLE

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

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}]]

CROSSREFS

Cf. A191107, A265100, A265104, A265159.

Sequence in context: A318244 A280395 A158991 * A303805 A304852 A305249

Adjacent sequences:  A265158 A265159 A265160 * A265162 A265163 A265164

KEYWORD

nonn,tabl

AUTHOR

L. Edson Jeffery, Dec 03 2015

STATUS

approved

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Last modified May 17 11:26 EDT 2022. Contains 353745 sequences. (Running on oeis4.)