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A241957
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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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4
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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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
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MATHEMATICA
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(* 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}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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