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A255168 Rectangular array A read by upward antidiagonals in which row n is the set of positive integers that are congruent to {(1 + 2^n*(3 + 2*(-1)^n))/3, 2^(n + 1), (1 + 2^n*(15 + 2*(-1)^n))/3} (mod 2^(n+2)). 1
1, 7, 4, 3, 8, 5, 27, 16, 15, 9, 11, 32, 19, 23, 12, 107, 64, 59, 35, 24, 13, 43, 128, 75, 91, 48, 31, 17, 427, 256, 235, 139, 96, 51, 39, 20, 171, 512, 299, 363, 192, 123, 67, 40, 21, 1707, 1024, 939, 555, 384, 203, 155, 80, 47, 25 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

A(n,k) = A(n,k-3) + 2^(n+2), n >= 1, k > 3, with initial conditions A(n,1) = (1 + 2^n*(3 + 2*(-1)^n))/3, A(n,2) = 2^(n+1), A(n,3) = A(n,1) + 2^(n+1).

A(n,k) == (1 + 2^n*(3 + 2*(-1)^n))/3 (mod 2^(n+1) or 2^(n+1) (mod 2^(n+2)).

EXAMPLE

Array A begins:

.       1     4     5     9    12    13    17     20     21     25

.       7     8    15    23    24    31    39     40     47     55

.       3    16    19    35    48    51    67     80     83     99

.      27    32    59    91    96   123   155    160    187    219

.      11    64    75   139   192   203   267    320    331    395

.     107   128   235   363   384   491   619    640    747    875

.      43   256   299   555   768   811  1067   1280   1323   1579

.     427   512   939  1451  1536  1963  2475   2560   2987   3499

.     171  1024  1195  2219  3072  3243  4267   5120   5291   6315

.    1707  2048  3755  5803  6144  7851  9899  10240  11947  13995

MATHEMATICA

(* Array antidiagonals flattened: *)

a[n_, 1] := (1 + 2^n*(3 + 2*(-1)^n))/3; a[n_, 2] := 2^(n + 1); a[n_, 3] := a[n, 1] + 2^(n + 1); a[n_, k_] := a[n, k - 3] + 2^(n + 2); Flatten[Table[a[n - k + 1, k], {n, 10}, {k, n}]]

CROSSREFS

A047610 (row 1).

Sequence in context: A244817 A293237 A199727 * A257776 A065477 A272526

Adjacent sequences:  A255165 A255166 A255167 * A255169 A255170 A255171

KEYWORD

nonn,tabl

AUTHOR

L. Edson Jeffery, May 04 2015

STATUS

approved

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Last modified February 21 12:59 EST 2018. Contains 299411 sequences. (Running on oeis4.)