A344264 When computing A229037, the value of the n-th term will add up to n-1 new constraints on the n-1 following terms; a(n) is the number of new constraints that the computation of A229037(n) brings.

0, 1, 2, 2, 2, 5, 5, 7, 7, 4, 4, 8, 3, 3, 9, 9, 16, 15, 9, 11, 12, 15, 15, 23, 12, 14, 23, 8, 7, 16, 6, 6, 15, 14, 26, 21, 5, 6, 10, 4, 4, 12, 11, 27, 24, 13, 19, 18, 34, 31, 49, 24, 28, 47, 46, 22, 19, 21, 23, 48, 18, 18, 44, 20, 39, 57, 47, 40, 38, 43, 46

Offset: 1

Author

Rémy Sigrist, May 13 2021

Keywords

• nonn

Comments

Once A229037(n) has been computed, we have the following constraints:

- for k = 1..n-1, A229037(n + k) <> 2*A229037(n) - A229037(n - k),

- if 2*A229037(n) - A229037(n - k) <= 0, then we ignore this constraint,

- if 2*A229037(n) - A229037(n - k) = 2*A229037(n') - A229037(n' - k')

for some n' < n and k' < n' such that n + k = n' + k',

then we also ignore this constraint.

Examples

			The first terms, alongside the corresponding value of A229037 (denoted by f(n)) and the new constraints, are:
  n  a(n)  f(n)  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19
  -  ----  ----  -  -  -  -  -  -  -  -  -  --  --  --  --  --  --  --  --  --  --
  1     0     1  .  .  .  .  .  .  .  .  .  .   .   .   .   .   .   .   .   .   .
  2     1     1  .  .  1  .  .  .  .  .  .  .   .   .   .   .   .   .   .   .   .
  3     2     2  .  .  .  3  3  .  .  .  .  .   .   .   .   .   .   .   .   .   .
  4     2     1  .  .  .  .  .  1  1  .  .  .   .   .   .   .   .   .   .   .   .
  5     2     1  .  .  .  .  .  .  .  1  1  .   .   .   .   .   .   .   .   .   .
  6     5     2  .  .  .  .  .  .  3  3  2   3   3  .   .   .   .   .   .   .   .
  7     5     2  .  .  .  .  .  .  .  2  3  .    2   3   3  .   .   .   .   .   .
  8     7     4  .  .  .  .  .  .  .  .  6   6   7   7   6   7   7  .   .   .   .
  9     7     4  .  .  .  .  .  .  .  .  .   4   6   6   7  .    6   7   7  .   .
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Scatterplot of the first 100000 terms
• Rémy Sigrist, PARI program for A344264

Crossrefs

Cf. A229037, A293866.

Programs

PARI

See Links section.

Formula

a(n) < n.