A361742 Lexicographically earliest sequence of nonnegative integers such that for any distinct m and n, the m X m square with lower left corner at (m, a(m)) and the n X n square with lower left corner at (n, a(n)) do not overlap (they can however touch).
0, 0, 2, 5, 9, 14, 20, 0, 27, 36, 46, 8, 57, 70, 84, 99, 115, 132, 150, 20, 169, 190, 212, 235, 259, 40, 284, 311, 339, 66, 368, 399, 431, 96, 464, 499, 535, 130, 572, 0, 611, 652, 694, 168, 737, 782, 828, 875, 923, 212, 972, 1023, 1075, 1128, 1182, 262, 1237
Offset: 1
Keywords
Examples
The first 8 boxes are arranged as follows (note that the X and Y axes have been swapped for practical reasons):
88888888
88888888
n 88888888 7777777
88888888 7777777
^ 88888888 6666667777777
| 88888888 6666667777777
| 88888888 555556666667777777
8 | 88888888 555556666667777777
7 | 4444555556666667777777
6 | 444455555666666
5 | 333444455555
4 | 3334444
3 | 22333
2 | 22
1 | 1
-------------------------------> a(n)
11111111112222222222
012345678901234567890123456789
.
so a(1) = a(2) = a(8) = 0,
a(3) = 2,
a(4) = 5,
a(5) = 9,
a(6) = 14,
a(7) = 20.
Links
- Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
- Rémy Sigrist, C++ program
- Rémy Sigrist, C++ program (faster)
- Rémy Sigrist, PARI program
Programs
-
PARI
See Links section.
Formula
a(n) < A000217(n).
Comments