A210635 Array read by descending antidiagonals: a(n,w) = ((w - (n mod w) - 1) + n) - (n mod w), n >= 0, w >= 1.
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, 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, 9, 7, 5, 3, 1, 11, 7, 11, 11, 11, 11, 12, 10, 8, 6, 4, 2, 0, 10, 6, 10, 10, 10, 12
Offset: 0
Examples
The transposed array begins: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ... 1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14 17 16 19 18 ... 2 1 0 5 4 3 8 7 6 11 10 9 14 13 12 17 16 15 20 19 ... 3 2 1 0 7 6 5 4 11 10 9 8 15 14 13 12 19 18 17 16 ... 4 3 2 1 0 9 8 7 6 5 14 13 12 11 10 19 18 17 16 15 ... 5 4 3 2 1 0 11 10 9 8 7 6 17 16 15 14 13 12 23 22 ... 6 5 4 3 2 1 0 13 12 11 10 9 8 7 20 19 18 17 16 15 ... 7 6 5 4 3 2 1 0 15 14 13 12 11 10 9 8 23 22 21 20 ... 8 7 6 5 4 3 2 1 0 17 16 15 14 13 12 11 10 9 26 25 ... 9 8 7 6 5 4 3 2 1 0 19 18 17 16 15 14 13 12 11 10 ......
Programs
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Maple
a:= (n,w) -> ((w - (n mod w) - 1) + n) - (n mod w): seq(seq(a(n,1+d-n), n=0..d), d=0..12); # Alois P. Heinz, Jun 07 2023
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PARI
a(n,w) = ((w - n % w - 1) + n) - n % w; matrix(7, 7, n, k, a(k-1, n)) \\ Michel Marcus, Jun 07 2023
Formula
a(n,w) = ((w - (n mod w) - 1) + n) - (n mod w).
Extensions
Edited by N. J. A. Sloane, Mar 26 2012
Entry revised by Editors of the OEIS, Jun 17 2023
Comments