A265159 Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = 5 + 9*A005836(2^(k - 1)*(2 n - 1)), n,k >= 1.

5, 32, 14, 86, 95, 41, 113, 257, 284, 122, 248, 338, 770, 851, 365, 275, 743, 1013, 2309, 2552, 1094, 329, 824, 2228, 3038, 6926, 7655, 3281, 356, 986, 2471, 6683, 9113, 20777, 22964, 9842, 734, 1067, 2957, 7412, 20048, 27338, 62330, 68891, 29525

Offset: 1

Author

L. Edson Jeffery, Dec 03 2015

Keywords

• nonn
• tabl

Comments

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

Examples

			Array A begins:
.      5    14    41    122    365    1094    3281     9842    29525
.     32    95   284    851   2552    7655   22964    68891   206672
.     86   257   770   2309   6926   20777   62330   186989   560966
.    113   338  1013   3038   9113   27338   82013   246038   738113
.    248   743  2228   6683  20048   60143  180428   541283  1623848
.    275   824  2471   7412  22235   66704  200111   600332  1800995
.    329   986  2957   8870  26609   79826  239477   718430  2155289
.    356  1067  3200   9599  28796   86387  259160   777479  2332436
.    734  2201  6602  19805  59414  178241  534722  1604165  4812494
		

Crossrefs

Cf. A005836, A055246, A265100, A265104, A265161.

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)]; Grid[Table[a265159[n, k], {n, 9}, {k, 9}]]
(* Array antidiagonals 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)]; Flatten[Table[a265159[n - k + 1, k], {n, 9}, {k, n}]]

Formula

Conjecture 2: A(n,k) = (A055246(n)*3^k + 1)/2, so the array and A265100 are related to Cantor's ternary set.

G.f. for row n (conjectured): f(n,x) = x*(A265100(n)-(A265100(n)+1)*x)/((1-x)*(1-3*x)).