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%I #15 Jun 09 2021 02:32:13
%S 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 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 46,22,19,21,23,48,18,18,44,20,39,57,47,40,38,43,46
%N 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 Once A229037(n) has been computed, we have the following constraints:
%C - for k = 1..n-1, A229037(n + k) <> 2*A229037(n) - A229037(n - k),
%C - if 2*A229037(n) - A229037(n - k) <= 0, then we ignore this constraint,
%C - if 2*A229037(n) - A229037(n - k) = 2*A229037(n') - A229037(n' - k')
%C for some n' < n and k' < n' such that n + k = n' + k',
%C then we also ignore this constraint.
%H Rémy Sigrist, <a href="/A344264/b344264.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A344264/a344264.png">Scatterplot of the first 100000 terms</a>
%H Rémy Sigrist, <a href="/A344264/a344264.gp.txt">PARI program for A344264</a>
%F a(n) < n.
%e The first terms, alongside the corresponding value of A229037 (denoted by f(n)) and the new constraints, are:
%e 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 - ---- ---- - - - - - - - - - -- -- -- -- -- -- -- -- -- --
%e 1 0 1 . . . . . . . . . . . . . . . . . . .
%e 2 1 1 . . 1 . . . . . . . . . . . . . . . .
%e 3 2 2 . . . 3 3 . . . . . . . . . . . . . .
%e 4 2 1 . . . . . 1 1 . . . . . . . . . . . .
%e 5 2 1 . . . . . . . 1 1 . . . . . . . . . .
%e 6 5 2 . . . . . . 3 3 2 3 3 . . . . . . . .
%e 7 5 2 . . . . . . . 2 3 . 2 3 3 . . . . . .
%e 8 7 4 . . . . . . . . 6 6 7 7 6 7 7 . . . .
%e 9 7 4 . . . . . . . . . 4 6 6 7 . 6 7 7 . .
%o (PARI) See Links section.
%Y Cf. A229037, A293866.
%K nonn
%O 1,3
%A _Rémy Sigrist_, May 13 2021