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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.

%I A329311 #12 Nov 13 2019 12:32:51
%S A329311 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,
%T A329311 1,1,11,24,780,1092,7644,11760,11760,311040,2736,64600,420,420,462,
%U A329311 157080,10626,483,210672,20,420,462,462,506,23,624,27,5292,45472,812
%N 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.
%C A329311 This sequence has fractal features; apparently, for any k > 0, the first k terms are repeated later (see illustration in Links section).
%H A329311 Rémy Sigrist, <a href="/A329311/b329311.txt">Table of n, a(n) for n = 1..10000</a>
%H A329311 Rémy Sigrist, <a href="/A329311/a329311.png">Logarithmic scatterplot of the first 80000 terms</a> (the two colored sections are equal up to an horizontal shift)
%e A329311 The first terms, alongside the corresponding k's, are:
%e A329311   n    a(n)     k's
%e A329311   ---  -------  ---------
%e A329311     1        1  {}
%e A329311     2        1  {}
%e A329311     3        1  {1}
%e A329311     4        1  {1}
%e A329311     5        2  {1, 2}
%e A329311     6        2  {2}
%e A329311     7        3  {1, 3}
%e A329311     8        1  {}
%e A329311     9        1  {}
%e A329311    10        1  {1}
%e A329311    11        1  {1}
%e A329311    12        8  {1, 2, 4}
%e A329311    13       10  {2, 5}
%e A329311    14       90  {3, 5, 6}
%e A329311    15       42  {6, 7}
%e A329311    16       42  {6, 7}
%e A329311    17       56  {1, 7, 8}
%o A329311 (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)) ", "))
%Y A329311 See A329257 for similar sequences.
%K A329311 nonn,look
%O A329311 1,5
%A A329311 _Rémy Sigrist_, Nov 10 2019