A329311 a(n) is the product of the numbers k such that a(n-2*k) = a(n-k) and 0 < n-2*k < n-k < n.

1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 8, 10, 90, 42, 42, 56, 56, 72, 9, 10, 1, 1, 1, 1, 2, 2, 3, 8, 1, 1, 1, 11, 24, 780, 1092, 7644, 11760, 11760, 311040, 2736, 64600, 420, 420, 462, 157080, 10626, 483, 210672, 20, 420, 462, 462, 506, 23, 624, 27, 5292, 45472, 812

Offset: 1

Author

Rémy Sigrist, Nov 10 2019

Keywords

• nonn
• look

Comments

This sequence has fractal features; apparently, for any k > 0, the first k terms are repeated later (see illustration in Links section).

Examples

			The first terms, alongside the corresponding k's, are:
  n    a(n)     k's
  ---  -------  ---------
    1        1  {}
    2        1  {}
    3        1  {1}
    4        1  {1}
    5        2  {1, 2}
    6        2  {2}
    7        3  {1, 3}
    8        1  {}
    9        1  {}
   10        1  {1}
   11        1  {1}
   12        8  {1, 2, 4}
   13       10  {2, 5}
   14       90  {3, 5, 6}
   15       42  {6, 7}
   16       42  {6, 7}
   17       56  {1, 7, 8}
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Logarithmic scatterplot of the first 80000 terms (the two colored sections are equal up to an horizontal shift)

Crossrefs

See A329257 for similar sequences.

Programs

PARI

for (n=1, #(a=vector(60)), print1 (a[n] = prod(k=1, (n-1)\2, if (a[n-k]==a[n-2*k], k, 1)) ", "))