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

Author

Rémy Sigrist, Mar 22 2023

Keywords

• nonn

Comments

This sequence is a variant of A361697.

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

Crossrefs

Cf. A000217, A289523, A361697.

Programs

PARI

See Links section.

Formula

a(n) < A000217(n).