cp's OEIS Frontend

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.

%I A241957 #40 Feb 07 2017 15:55:01
%S A241957 1,3,5,7,11,9,15,23,19,13,31,47,39,27,17,63,95,79,55,35,21,127,191,
%T A241957 159,111,71,43,25,255,383,319,223,143,87,51,29,511,767,639,447,287,
%U A241957 175,103,59,33,1023,1535,1279,895,575,351,207,119,67,37
%N 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.
%C A241957 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.
%C A241957 For j a natural number, 2*j - 1 appears in row A001511(j) of A.
%C A241957 This is the square array A075300 with the first row omitted. - _Peter Bala_, Feb 07 2017
%H A241957 Vincenzo Librandi, <a href="/A241957/b241957.txt">Rows n = 0..50, flattened</a>
%H A241957 <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>.
%F A241957 A(n,k) = 2*A054582(n-1,k-1) - 1.
%e A241957 Array begins:
%e A241957 .      1     5     9    13    17     21     25     29     33     37
%e A241957 .      3    11    19    27    35     43     51     59     67     75
%e A241957 .      7    23    39    55    71     87    103    119    135    151
%e A241957 .     15    47    79   111   143    175    207    239    271    303
%e A241957 .     31    95   159   223   287    351    415    479    543    607
%e A241957 .     63   191   319   447   575    703    831    959   1087   1215
%e A241957 .    127   383   639   895  1151   1407   1663   1919   2175   2431
%e A241957 .    255   767  1279  1791  2303   2815   3327   3839   4351   4863
%e A241957 .    511  1535  2559  3583  4607   5631   6655   7679   8703   9727
%e A241957 .   1023  3071  5119  7167  9215  11263  13311  15359  17407  19455
%t A241957 (* Array: *)
%t A241957 Grid[Table[2^n*(2*k - 1) - 1, {n, 10}, {k, 10}]]
%t A241957 (* Array antidiagonals flattened: *)
%t A241957 Flatten[Table[2^(n - k + 1)*(2*k - 1) - 1, {n, 10}, {k, n}]]
%Y A241957 Cf. A016813, A017101 (rows 1 and 2).
%Y A241957 Cf. A000225, A083329, A153894, A086224, A052996, etc. (columns 1-5).
%Y A241957 Cf. A005408 (odd natural numbers), A054582.
%Y A241957 Cf. A075300.
%K A241957 nonn,tabl,easy
%O A241957 1,2
%A A241957 _L. Edson Jeffery_, Aug 09 2014