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A344322 a(n) is the number of forbidden values when computing A229037(n).

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%I A344322 #13 Aug 27 2024 18:31:10
%S A344322 0,0,1,1,1,1,2,3,4,3,4,4,3,2,3,3,4,4,4,5,5,6,6,7,8,7,9,9,8,9,9,9,8,9,
%T A344322 9,8,8,8,8,7,8,6,8,9,7,8,9,7,9,8,9,9,8,9,10,10,11,10,11,11,11,11,11,
%U A344322 11,13,15,14,14,13,15,17,16,17,15,16,17,16,16,17
%N A344322 a(n) is the number of forbidden values when computing A229037(n).
%C A344322 In other words, a(n) is the number of distinct positive terms of the form 2*A229037(n - k) - A229037(n - 2*k) with n > 2*k > 0.
%H A344322 Rémy Sigrist, <a href="/A344322/b344322.txt">Table of n, a(n) for n = 1..10000</a>
%H A344322 Rémy Sigrist, <a href="/A344322/a344322.gp.txt">PARI program for A344322</a>
%e A344322 For n=14, we have:
%e A344322 - 2*A229037(13) - A229037(12) = 2*1 - 2 = 0,
%e A344322 - 2*A229037(12) - A229037(10) = 2*2 - 1 = 3,
%e A344322 - 2*A229037(11) - A229037(8) = 2*1 - 4 = -2,
%e A344322 - 2*A229037(10) - A229037(6) = 2*1 - 2 = 0,
%e A344322 - 2*A229037(9) - A229037(4) = 2*4 - 1 = 7,
%e A344322 - 2*A229037(8) - A229037(2) = 2*4 - 1 = 7,
%e A344322 - so a(14) = #{3, 7} = 2.
%o A344322 (PARI) \\ See Links section.
%Y A344322 Cf. A229037, A293866, A344264.
%K A344322 nonn
%O A344322 1,7
%A A344322 _Rémy Sigrist_, May 15 2021