A317585 a(n) = number of k with 1 <= k <= n-1 such that abs(a(k) - a(n-k)) <= 2.

0, 1, 2, 3, 2, 5, 4, 3, 2, 9, 6, 7, 6, 5, 2, 5, 6, 9, 4, 9, 2, 13, 12, 13, 8, 7, 6, 11, 6, 13, 2, 9, 8, 7, 8, 13, 4, 13, 6, 15, 6, 11, 12, 13, 16, 23, 8, 13, 0, 17, 14, 25, 14, 13, 8, 7, 6, 19, 8, 19, 6, 13, 4, 19, 12, 25, 20, 23, 10, 19, 10, 21, 16, 23, 10

Offset: 1

Author

Rémy Sigrist, Aug 01 2018

Keywords

• nonn

Comments

See A317420 for similar sequences.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Colored scatterplot of the first 100000 terms (where the color is function of the parity of n)

Crossrefs

Cf. A317420.

Programs

PARI

a = vector(75); for (n=1, #a, a[n] = sum(k=1, n-1, abs(a[k]-a[n-k])<=2); print1 (a[n] ", "))

Formula

For n = 5:

- |a(1) - a(4)| = |0 - 3| = 3 > 2,

- |a(2) - a(3)| = |1 - 2| = 1 <= 2,

- |a(3) - a(2)| = |2 - 1| = 1 <= 2,

- |a(4) - a(1)| = |3 - 0| = 3 > 2,

- hence a(5) = 2.