A254067 - OEIS

A254067

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.

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

1,2

COMMENTS

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).

LINKS

Table of n, a(n) for n=1..55.

FORMULA

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.

EXAMPLE

. 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

MATHEMATICA

(* 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}]]

CROSSREFS

Sequence in context: A299618 A376875 A021926 * A376658 A178727 A354917

Adjacent sequences: A254064 A254065 A254066 * A254068 A254069 A254070

KEYWORD

nonn,tabl

AUTHOR

L. Edson Jeffery, May 02 2015

STATUS

approved