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%I #12 Dec 04 2015 13:06:06
%S 5,32,14,86,95,41,113,257,284,122,248,338,770,851,365,275,743,1013,
%T 2309,2552,1094,329,824,2228,3038,6926,7655,3281,356,986,2471,6683,
%U 9113,20777,22964,9842,734,1067,2957,7412,20048,27338,62330,68891,29525
%N 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 Conjecture 1: The array contains without duplication all possible "block numbers" defined in A265100.
%F Conjecture 2: A(n,k) = (A055246(n)*3^k + 1)/2, so the array and A265100 are related to Cantor's ternary set.
%F G.f. for row n (conjectured): f(n,x) = x*(A265100(n)-(A265100(n)+1)*x)/((1-x)*(1-3*x)).
%e Array A begins:
%e . 5 14 41 122 365 1094 3281 9842 29525
%e . 32 95 284 851 2552 7655 22964 68891 206672
%e . 86 257 770 2309 6926 20777 62330 186989 560966
%e . 113 338 1013 3038 9113 27338 82013 246038 738113
%e . 248 743 2228 6683 20048 60143 180428 541283 1623848
%e . 275 824 2471 7412 22235 66704 200111 600332 1800995
%e . 329 986 2957 8870 26609 79826 239477 718430 2155289
%e . 356 1067 3200 9599 28796 86387 259160 777479 2332436
%e . 734 2201 6602 19805 59414 178241 534722 1604165 4812494
%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)]; Grid[Table[a265159[n, k], {n, 9}, {k, 9}]]
%t (* Array antidiagonals 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)]; Flatten[Table[a265159[n - k + 1, k], {n, 9}, {k, n}]]
%Y Cf. A005836, A055246, A265100, A265104, A265161.
%K nonn,tabl
%O 1,1
%A _L. Edson Jeffery_, Dec 03 2015
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