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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.

%I A344264 #15 Jun 09 2021 02:32:13
%S A344264 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,
%T A344264 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,
%U A344264 46,22,19,21,23,48,18,18,44,20,39,57,47,40,38,43,46
%N 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.
%C A344264 Once A229037(n) has been computed, we have the following constraints:
%C A344264 - for k = 1..n-1, A229037(n + k) <> 2*A229037(n) - A229037(n - k),
%C A344264    - if 2*A229037(n) - A229037(n - k) <= 0, then we ignore this constraint,
%C A344264    - if 2*A229037(n) - A229037(n - k) = 2*A229037(n') - A229037(n' - k')
%C A344264      for some n' < n and k' < n' such that n + k = n' + k',
%C A344264      then we also ignore this constraint.
%H A344264 Rémy Sigrist, <a href="/A344264/b344264.txt">Table of n, a(n) for n = 1..10000</a>
%H A344264 Rémy Sigrist, <a href="/A344264/a344264.png">Scatterplot of the first 100000 terms</a>
%H A344264 Rémy Sigrist, <a href="/A344264/a344264.gp.txt">PARI program for A344264</a>
%F A344264 a(n) < n.
%e A344264 The first terms, alongside the corresponding value of A229037 (denoted by f(n)) and the new constraints, are:
%e A344264   n  a(n)  f(n)  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19
%e A344264   -  ----  ----  -  -  -  -  -  -  -  -  -  --  --  --  --  --  --  --  --  --  --
%e A344264   1     0     1  .  .  .  .  .  .  .  .  .  .   .   .   .   .   .   .   .   .   .
%e A344264   2     1     1  .  .  1  .  .  .  .  .  .  .   .   .   .   .   .   .   .   .   .
%e A344264   3     2     2  .  .  .  3  3  .  .  .  .  .   .   .   .   .   .   .   .   .   .
%e A344264   4     2     1  .  .  .  .  .  1  1  .  .  .   .   .   .   .   .   .   .   .   .
%e A344264   5     2     1  .  .  .  .  .  .  .  1  1  .   .   .   .   .   .   .   .   .   .
%e A344264   6     5     2  .  .  .  .  .  .  3  3  2   3   3  .   .   .   .   .   .   .   .
%e A344264   7     5     2  .  .  .  .  .  .  .  2  3  .    2   3   3  .   .   .   .   .   .
%e A344264   8     7     4  .  .  .  .  .  .  .  .  6   6   7   7   6   7   7  .   .   .   .
%e A344264   9     7     4  .  .  .  .  .  .  .  .  .   4   6   6   7  .    6   7   7  .   .
%o A344264 (PARI) See Links section.
%Y A344264 Cf. A229037, A293866.
%K A344264 nonn
%O A344264 1,3
%A A344264 _Rémy Sigrist_, May 13 2021