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A210635 Array read by descending antidiagonals: a(n,w) = ((w - (n mod w) - 1) + n) - (n mod w), n >= 0, w >= 1.

%I A210635 #45 Jun 17 2023 22:54:57
%S A210635 0,1,1,2,0,2,3,1,3,3,4,2,0,2,4,5,3,1,5,5,5,6,4,2,0,4,4,6,7,5,3,1,7,3,
%T A210635 7,7,8,6,4,2,0,6,8,6,8,9,7,5,3,1,9,5,7,9,9,10,8,6,4,2,0,8,4,6,8,10,11,
%U A210635 9,7,5,3,1,11,7,11,11,11,11,12,10,8,6,4,2,0,10,6,10,10,10,12
%N A210635 Array read by descending antidiagonals: a(n,w) = ((w - (n mod w) - 1) + n) - (n mod w), n >= 0, w >= 1.
%C A210635 Each column is a permutation of the nonnegative integers.
%C A210635 Column w can be used to mirror horizontally an infinite rectangular image of width w stored in a array of pixels. The pixels in the first row of the image are numbered from 0 to w-1 and subsequent rows continue the numbering likewise.
%F A210635 a(n,w) = ((w - (n mod w) - 1) + n) - (n mod w).
%e A210635 The transposed array begins:
%e A210635   0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 ...
%e A210635   1  0  3  2  5  4  7  6  9  8 11 10 13 12 15 14 17 16 19 18 ...
%e A210635   2  1  0  5  4  3  8  7  6 11 10  9 14 13 12 17 16 15 20 19 ...
%e A210635   3  2  1  0  7  6  5  4 11 10  9  8 15 14 13 12 19 18 17 16 ...
%e A210635   4  3  2  1  0  9  8  7  6  5 14 13 12 11 10 19 18 17 16 15 ...
%e A210635   5  4  3  2  1  0 11 10  9  8  7  6 17 16 15 14 13 12 23 22 ...
%e A210635   6  5  4  3  2  1  0 13 12 11 10  9  8  7 20 19 18 17 16 15 ...
%e A210635   7  6  5  4  3  2  1  0 15 14 13 12 11 10  9  8 23 22 21 20 ...
%e A210635   8  7  6  5  4  3  2  1  0 17 16 15 14 13 12 11 10  9 26 25 ...
%e A210635   9  8  7  6  5  4  3  2  1  0 19 18 17 16 15 14 13 12 11 10 ......
%p A210635 a:= (n,w) ->  ((w - (n mod w) - 1) + n) - (n mod w):
%p A210635 seq(seq(a(n,1+d-n), n=0..d), d=0..12);  # _Alois P. Heinz_, Jun 07 2023
%o A210635 (PARI) a(n,w) = ((w - n % w - 1) + n) - n % w;
%o A210635 matrix(7, 7, n, k, a(k-1, n)) \\ _Michel Marcus_, Jun 07 2023
%Y A210635 Column 2: A004442, column 3: A330396, column 4: A004444, column 8: A004448.
%K A210635 nonn,easy,tabl
%O A210635 0,4
%A A210635 _Lucas Beristayn_, Mar 25 2012
%E A210635 Edited by _N. J. A. Sloane_, Mar 26 2012
%E A210635 Entry revised by Editors of the OEIS, Jun 17 2023