A257791 Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = 2^(n+1)*(2*k - 1), n,k >= 1.

4, 8, 12, 16, 24, 20, 32, 48, 40, 28, 64, 96, 80, 56, 36, 128, 192, 160, 112, 72, 44, 256, 384, 320, 224, 144, 88, 52, 512, 768, 640, 448, 288, 176, 104, 60, 1024, 1536, 1280, 896, 576, 352, 208, 120, 68, 2048, 3072, 2560, 1792, 1152, 704, 416, 240, 136, 76

Offset: 1

Author

L. Edson Jeffery, May 08 2015

Keywords

• nonn
• tabl

Comments

Lemma: The sequence is a permutation of A008586\{0} = {4*m : m = 1,2,...}.

Proof: Write A(n,k)/4 = A054582(n-1,k-1). The sequence A054582 is known to be a permutation of the natural numbers, and the result follows. QED

Examples

			Array A begins:
.       4    12     20     28     36     44     52     60     68     76
.       8    24     40     56     72     88    104    120    136    152
.      16    48     80    112    144    176    208    240    272    304
.      32    96    160    224    288    352    416    480    544    608
.      64   192    320    448    576    704    832    960   1088   1216
.     128   384    640    896   1152   1408   1664   1920   2176   2432
.     256   768   1280   1792   2304   2816   3328   3840   4352   4864
.     512  1536   2560   3584   4608   5632   6656   7680   8704   9728
.    1024  3072   5120   7168   9216  11264  13312  15360  17408  19456
.    2048  6144  10240  14336  18432  22528  26624  30720  34816  38912
		

Crossrefs

Cf. A000079 (powers of 2), A005408 (odd numbers), A008586 (multiples of 4), A014480, A054582.

Cf. A257499.

Programs

Mathematica

(* Array: *)
A257791[n_, k_] := 2^(n + 1)*(2*k - 1); Grid[Table[A257791[n, k], {n, 10}, {k, 10}]]
(* Array antidiagonals flattened: *)
Flatten[Table[2^(n - k + 2)*(2*k - 1), {n, 10}, {k, n}]]

Formula

A(n,n) = 4*A014480(n-1).