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, 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

Offset: 1

Author

L. Edson Jeffery, May 04 2015

Keywords

• nonn
• tabl

Examples

			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
		

Crossrefs

A047610 (row 1).

Programs

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}]]

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)).