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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.

%I A265161 #9 Dec 04 2015 23:17:18
%S A265161 8,35,26,89,107,80,116,269,323,242,251,350,809,971,728,278,755,1052,
%T A265161 2429,2915,2186,332,836,2267,3158,7289,8747,6560,359,998,2510,6803,
%U A265161 9476,21869,26243,19682,737,1079,2996,7532,20411,28430,65609,78731,59048
%N 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.
%C A265161 Conjecture 1: The array contains without duplication all possible "gap numbers" as defined in A265100.
%F A265161 Conjecture 2: A(n,k) = A191107(n)*3^k - 1.
%e A265161 Array A begins:
%e A265161 .      8    26    80    242    728    2186    6560    19682    59048
%e A265161 .     35   107   323    971   2915    8747   26243    78731   236195
%e A265161 .     89   269   809   2429   7289   21869   65609   196829   590489
%e A265161 .    116   350  1052   3158   9476   28430   85292   255878   767636
%e A265161 .    251   755  2267   6803  20411   61235  183707   551123  1653371
%e A265161 .    278   836  2510   7532  22598   67796  203390   610172  1830518
%e A265161 .    332   998  2996   8990  26972   80918  242756   728270  2184812
%e A265161 .    359  1079  3239   9719  29159   87479  262439   787319  2361959
%e A265161 .    737  2213  6641  19925  59777  179333  538001  1614005  4842017
%t A265161 (* Array: *)
%t A265161 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}]]
%t A265161 (* Array antidiagonal flattened: *)
%t A265161 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}]]
%Y A265161 Cf. A191107, A265100, A265104, A265159.
%K A265161 nonn,tabl
%O A265161 1,1
%A A265161 _L. Edson Jeffery_, Dec 03 2015