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A265159
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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.
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2
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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
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OFFSET
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1,1
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COMMENTS
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Conjecture 1: The array contains without duplication all possible "block numbers" defined in A265100.
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LINKS
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FORMULA
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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)).
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EXAMPLE
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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
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MATHEMATICA
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(* 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}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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