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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).
2
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
1,3
COMMENTS
This sequence is a variant of A361697.
LINKS
Rémy Sigrist, C++ program
Rémy Sigrist, C++ program (faster)
Rémy Sigrist, PARI program
FORMULA
a(n) < A000217(n).
EXAMPLE
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.
PROG
(C++) See Links section.
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Mar 22 2023
STATUS
approved