A241957 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*(2*k - 1) - 1, n,k >= 1.

1, 3, 5, 7, 11, 9, 15, 23, 19, 13, 31, 47, 39, 27, 17, 63, 95, 79, 55, 35, 21, 127, 191, 159, 111, 71, 43, 25, 255, 383, 319, 223, 143, 87, 51, 29, 511, 767, 639, 447, 287, 175, 103, 59, 33, 1023, 1535, 1279, 895, 575, 351, 207, 119, 67, 37

Offset

1,2

Comments

The sequence is a permutation of the odd natural numbers, since A(n,k) = 2*A054582(n-1,k-1) - 1 and A054582 is a permutation of the natural numbers.

For j a natural number, 2*j - 1 appears in row A001511(j) of A.

This is the square array A075300 with the first row omitted. - Peter Bala, Feb 07 2017

Links

Vincenzo Librandi, Rows n = 0..50, flattened

Index entries for sequences related to 3x+1 (or Collatz) problem.

Formula

A(n,k) = 2*A054582(n-1,k-1) - 1.

Example

Array begins:
.      1     5     9    13    17     21     25     29     33     37
.      3    11    19    27    35     43     51     59     67     75
.      7    23    39    55    71     87    103    119    135    151
.     15    47    79   111   143    175    207    239    271    303
.     31    95   159   223   287    351    415    479    543    607
.     63   191   319   447   575    703    831    959   1087   1215
.    127   383   639   895  1151   1407   1663   1919   2175   2431
.    255   767  1279  1791  2303   2815   3327   3839   4351   4863
.    511  1535  2559  3583  4607   5631   6655   7679   8703   9727
.   1023  3071  5119  7167  9215  11263  13311  15359  17407  19455

Mathematica

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

Crossrefs

Cf. A016813, A017101 (rows 1 and 2).

Cf. A000225, A083329, A153894, A086224, A052996, etc. (columns 1-5).

Cf. A005408 (odd natural numbers), A054582.

Cf. A075300.

Sequence in context: A338842 A022457 A066066 * A112070 A208643 A375345

Adjacent sequences: A241954 A241955 A241956 * A241958 A241959 A241960

Keyword

nonn,tabl,easy

Author

L. Edson Jeffery, Aug 09 2014

Status

approved