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