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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. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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: A273635 A299618 A021926 * A178727 A243446 A154188

Adjacent sequences:  A254064 A254065 A254066 * A254068 A254069 A254070

KEYWORD

nonn,tabl

AUTHOR

L. Edson Jeffery, May 02 2015

STATUS

approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)