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A254312
Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = (2^a(n)*(6*k - (3 - (-1)^a(n))*(1 - (-1)^n)/2) - 2^n + 4)/6, n,k >= 1, where {a(n)} is the Beatty sequence A117630 defined by a(n) = floor(n*log(3)/log(3/2)).
4
3, 32, 7, 170, 64, 11, 1022, 426, 96, 15, 2726, 2046, 682, 128, 19, 65526, 10918, 3070, 938, 160, 23, 174742, 131062, 19110, 4094, 1194, 192, 27, 2097110, 436886, 196598, 27302, 5118, 1450, 224, 31, 11184726, 4194262, 699030, 262134, 35494, 6142, 1706, 256, 35
OFFSET
1,1
COMMENTS
Conjecture: The array A contains without duplication all natural numbers m such that m < S(m), where the function S is as defined in A257480; i.e., the sequence is a permutation of A254311.
EXAMPLE
Array A begins:
. 3 7 11 15 19 23 27 31
. 32 64 96 128 160 192 224 256
. 170 426 682 938 1194 1450 1706 1962
. 1022 2046 3070 4094 5118 6142 7166 8190
. 2726 10918 19110 27302 35494 43686 51878 60070
. 65526 131062 196598 262134 327670 393206 458742 524278
. 174742 436886 699030 961174 1223318 1485462 1747606 2009750
. 2097110 4194262 6291414 8388566 10485718 12582870 14680022 16777174
MATHEMATICA
(* Array antidiagonals flattened: *)
a[n_] := Floor[n*Log[3/2, 3]]; A254312[n_, k_] := (2^a[n]*(6*k - (3 - (-1)^a[n])*(1 - (-1)^n)/2) - 2^n + 4)/6; Flatten[Table[A254312[n - k + 1, k], {n, 9}, {k, n}]]
CROSSREFS
Cf. A004767, A174312 (rows 1 and 2).
Sequence in context: A173649 A210648 A119937 * A304048 A324223 A197368
KEYWORD
nonn,tabl
AUTHOR
L. Edson Jeffery, May 03 2015
STATUS
approved