A335190 a(n) is the number of values of k < n for which 4*(a(k) + a(n-k)) <= n.

0, 1, 0, 2, 2, 1, 2, 6, 2, 4, 0, 5, 4, 2, 6, 8, 4, 7, 2, 8, 6, 3, 10, 12, 6, 10, 4, 11, 8, 4, 12, 14, 8, 13, 6, 14, 10, 5, 14, 18, 10, 14, 8, 17, 10, 10, 18, 20, 14, 17, 12, 20, 10, 13, 16, 22, 16, 14, 14, 25, 10, 14, 16, 24, 22, 19, 16, 28, 12, 17, 20, 30, 24

Offset

1,4

Comments

This sequence is a variant of A335060.

Graphically, we have an overlay of four curves that correspond to the quadrisections of the sequence.

Links

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

Rémy Sigrist, Colored scatterplot of the first 100000 terms

Example

The first terms, alongside the corresponding k's, are:
  n   a(n)  k's
  --  ----  ---------------------
   1     0  {}
   2     1  {1}
   3     0  {}
   4     2  {1, 3}
   5     2  {2, 3}
   6     1  {3}
   7     2  {1, 6}
   8     6  {1, 2, 3, 5, 6, 7}
   9     2  {3, 6}
  10     4  {1, 3, 7, 9}
  11     0  {}
  12     5  {1, 3, 6, 9, 11}

Prog

(PARI) for (n=1, #a=vector(73), print1 (a[n]=sum(k=1, n-1, a[k]+a[n-k]<=n/4)", "))

Crossrefs

Cf. A335060.

Sequence in context: A091562 A106585 A057227 * A283170 A368836 A336823

Adjacent sequences: A335187 A335188 A335189 * A335191 A335192 A335193

Keyword

nonn,look

Author

Rémy Sigrist, May 26 2020

Status

approved