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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.
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%I #40 Feb 07 2017 15:55:01

%S 1,3,5,7,11,9,15,23,19,13,31,47,39,27,17,63,95,79,55,35,21,127,191,

%T 159,111,71,43,25,255,383,319,223,143,87,51,29,511,767,639,447,287,

%U 175,103,59,33,1023,1535,1279,895,575,351,207,119,67,37

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

%C This is the square array A075300 with the first row omitted. - _Peter Bala_, Feb 07 2017

%H Vincenzo Librandi, <a href="/A241957/b241957.txt">Rows n = 0..50, flattened</a>

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

%e Array begins:

%e . 1 5 9 13 17 21 25 29 33 37

%e . 3 11 19 27 35 43 51 59 67 75

%e . 7 23 39 55 71 87 103 119 135 151

%e . 15 47 79 111 143 175 207 239 271 303

%e . 31 95 159 223 287 351 415 479 543 607

%e . 63 191 319 447 575 703 831 959 1087 1215

%e . 127 383 639 895 1151 1407 1663 1919 2175 2431

%e . 255 767 1279 1791 2303 2815 3327 3839 4351 4863

%e . 511 1535 2559 3583 4607 5631 6655 7679 8703 9727

%e . 1023 3071 5119 7167 9215 11263 13311 15359 17407 19455

%t (* Array: *)

%t Grid[Table[2^n*(2*k - 1) - 1, {n, 10}, {k, 10}]]

%t (* Array antidiagonals flattened: *)

%t Flatten[Table[2^(n - k + 1)*(2*k - 1) - 1, {n, 10}, {k, n}]]

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

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

%Y Cf. A005408 (odd natural numbers), A054582.

%Y Cf. A075300.

%K nonn,tabl,easy

%O 1,2

%A _L. Edson Jeffery_, Aug 09 2014