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

1,7

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A344322

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A229037, A293866, A344264.

Sequence in context: A324197 A259573 A108015 * A030398 A030384 A067349

Adjacent sequences: A344319 A344320 A344321 * A344323 A344324 A344325

Keyword

nonn

Author

Rémy Sigrist, May 15 2021

Status

approved