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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
OFFSET
1,1
COMMENTS
Conjecture 1: The array contains without duplication all possible "gap numbers" as defined in A265100.
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
KEYWORD
nonn,tabl
AUTHOR
L. Edson Jeffery, Dec 03 2015
STATUS
approved