A344322 a(n) is the number of forbidden values when computing A229037(n).

0, 0, 1, 1, 1, 1, 2, 3, 4, 3, 4, 4, 3, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 8, 7, 9, 9, 8, 9, 9, 9, 8, 9, 9, 8, 8, 8, 8, 7, 8, 6, 8, 9, 7, 8, 9, 7, 9, 8, 9, 9, 8, 9, 10, 10, 11, 10, 11, 11, 11, 11, 11, 11, 13, 15, 14, 14, 13, 15, 17, 16, 17, 15, 16, 17, 16, 16, 17

Offset: 1

Author

Rémy Sigrist, May 15 2021

Keywords

• nonn

Comments

In other words, a(n) is the number of distinct positive terms of the form 2*A229037(n - k) - A229037(n - 2*k) with n > 2*k > 0.

Examples

			For n=14, we have:
- 2*A229037(13) - A229037(12) = 2*1 - 2 = 0,
- 2*A229037(12) - A229037(10) = 2*2 - 1 = 3,
- 2*A229037(11) - A229037(8) = 2*1 - 4 = -2,
- 2*A229037(10) - A229037(6) = 2*1 - 2 = 0,
- 2*A229037(9) - A229037(4) = 2*4 - 1 = 7,
- 2*A229037(8) - A229037(2) = 2*4 - 1 = 7,
- so a(14) = #{3, 7} = 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A344322

Crossrefs

Cf. A229037, A293866, A344264.

Programs

PARI

\\ See Links section.