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A254067
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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) = S(4*A257499(n,k) - 3), n,k >= 1, where the function S is as defined in A257480.
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4
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1, 8, 4, 5, 17, 7, 68, 32, 26, 10, 41, 149, 59, 35, 13, 608, 284, 230, 86, 44, 16, 365, 1337, 527, 311, 113, 53, 19, 5468, 2552, 2066, 770, 392, 140, 62, 22, 3281, 12029, 4739, 2795, 1013, 473, 167, 71, 25, 49208, 22964, 18590, 6926, 3524, 1256, 554, 194, 80, 28
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OFFSET
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1,2
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COMMENTS
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Theorem: For all indices n and k such that n + k > 2, log(A(n,k))/log(A257499(n,k)) < log_2(3).
Conjecture: Arranging the sequence in ascending order gives A189707 (positions of 0 in A189706).
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LINKS
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FORMULA
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A(n,k) = S(4*A257499(n,k) - 3) = (3 + 3^n*(6*k - 3 + 2*(-1)^n))/6, where the function S is as defined in A257480.
For all k, A(1,k) <= A257499(1,k), and A(n,k) > A257499(n,k), for all n > 1.
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EXAMPLE
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. 1 4 7 10 13 16 19 22 25 28
. 8 17 26 35 44 53 62 71 80 89
. 5 32 59 86 113 140 167 194 221 248
. 68 149 230 311 392 473 554 635 716 797
. 41 284 527 770 1013 1256 1499 1742 1985 2228
. 608 1337 2066 2795 3524 4253 4982 5711 6440 7169
. 365 2552 4739 6926 9113 11300 13487 15674 17861 20048
. 5468 12029 18590 25151 31712 38273 44834 51395 57956 64517
. 3281 22964 42647 62330 82013 101696 121379 141062 160745 180428
. 49208 108257 167306 226355 285404 344453 403502 462551 521600 580649
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MATHEMATICA
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(* Array antidiagonals flattened: *)
v[x_] := IntegerExponent[x, 2]; f[x_] := (3*x + 1)/2^v[3*x + 1]; s[x_] := (3 + (3/2)^v[1 + f[x]] (1 + f[x]))/6; A257499[n_, k_] := (1 + 2^n*(6*k - 3 + 2*(-1)^n))/3; A254067[n_, k_] := s[4*A257499[n, k] - 3]; Flatten[Table[A254067[n - k + 1, k], {n, 10}, {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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