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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.

%I A265159 #12 Dec 04 2015 13:06:06
%S A265159 5,32,14,86,95,41,113,257,284,122,248,338,770,851,365,275,743,1013,
%T A265159 2309,2552,1094,329,824,2228,3038,6926,7655,3281,356,986,2471,6683,
%U A265159 9113,20777,22964,9842,734,1067,2957,7412,20048,27338,62330,68891,29525
%N 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.
%C A265159 Conjecture 1: The array contains without duplication all possible "block numbers" defined in A265100.
%F A265159 Conjecture 2: A(n,k) = (A055246(n)*3^k + 1)/2, so the array and A265100 are related to Cantor's ternary set.
%F A265159 G.f. for row n (conjectured): f(n,x) = x*(A265100(n)-(A265100(n)+1)*x)/((1-x)*(1-3*x)).
%e A265159 Array A begins:
%e A265159 .      5    14    41    122    365    1094    3281     9842    29525
%e A265159 .     32    95   284    851   2552    7655   22964    68891   206672
%e A265159 .     86   257   770   2309   6926   20777   62330   186989   560966
%e A265159 .    113   338  1013   3038   9113   27338   82013   246038   738113
%e A265159 .    248   743  2228   6683  20048   60143  180428   541283  1623848
%e A265159 .    275   824  2471   7412  22235   66704  200111   600332  1800995
%e A265159 .    329   986  2957   8870  26609   79826  239477   718430  2155289
%e A265159 .    356  1067  3200   9599  28796   86387  259160   777479  2332436
%e A265159 .    734  2201  6602  19805  59414  178241  534722  1604165  4812494
%t A265159 (* Array: *)
%t A265159 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}]]
%t A265159 (* Array antidiagonals flattened: *)
%t A265159 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}]]
%Y A265159 Cf. A005836, A055246, A265100, A265104, A265161.
%K A265159 nonn,tabl
%O A265159 1,1
%A A265159 _L. Edson Jeffery_, Dec 03 2015