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A317596 a(n) is the number of k with 1 <= k <= n-1 such that a(k) + 2 * a(n-k) <= n.

%I A317596 #11 Aug 06 2018 19:51:42
%S A317596 0,1,2,3,3,4,4,5,6,6,7,7,8,8,9,10,11,12,13,14,14,15,15,15,15,16,16,16,
%T A317596 17,17,17,18,18,18,18,19,20,23,25,29,31,33,34,36,37,37,37,37,37,37,37,
%U A317596 37,37,37,37,37,37,37,37,37,38,38,38,38,38,39,39,39,39
%N A317596 a(n) is the number of k with 1 <= k <= n-1 such that a(k) + 2 * a(n-k) <= n.
%C A317596 See A317582 for similar sequences.
%H A317596 Rémy Sigrist, <a href="/A317596/b317596.txt">Table of n, a(n) for n = 1..10000</a>
%e A317596 For n = 5:
%e A317596 - a(1) + 2 * a(4) = 0 + 2 * 3 = 6 > 5,
%e A317596 - a(2) + 2 * a(3) = 1 + 2 * 2 = 5 <= 5,
%e A317596 - a(3) + 2 * a(2) = 2 + 2 * 1 = 4 <= 5,
%e A317596 - a(4) + 2 * a(1) = 3 + 2 * 0 = 3 <= 5,
%e A317596 - hence a(5) = 3.
%t A317596 a[n_] := a[n] = Length@ Select[ Range[n - 1], a[#] + 2a[n - #] <= n &]; a[0] = 0; Array[a, 70] (* _Robert G. Wilson v_, Aug 03 2018 *)
%o A317596 (PARI) a = vector(73); for (n=1, #a, a[n] = sum(k=1, n-1, a[k] + 2*a[n-k] <= n); print1 (a[n] ", "))
%Y A317596 Cf. A317582.
%K A317596 nonn
%O A317596 1,3
%A A317596 _Rémy Sigrist_, Aug 01 2018