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A350105 Number of subsets of the initial segment of the natural numbers strictly below n which are not self-measuring. Number of subsets S of [n] with S != distset(S).

%I A350105 #12 Feb 01 2024 08:39:04
%S A350105 0,0,1,3,9,22,52,112,238,490,999,2019,4065,8155,16345,32725,65489,
%T A350105 131020,262090,524228,1048514,2097084,4194232,8388532,16777138,
%U A350105 33554346,67108775,134217635,268435359,536870809,1073741719,2147483535,4294967181,8589934471,17179869059
%N A350105 Number of subsets of the initial segment of the natural numbers strictly below n which are not self-measuring. Number of subsets S of [n] with S != distset(S).
%C A350105 We use the notation [n] = {0, 1, ..., n-1}. If S is a subset of [n] then we define the distset of S (set of distances of S) as {|x - y|: x, y in S}. We call a subset S of the natural numbers self-measuring if and only if S = distset(S).
%H A350105 Winston de Greef, <a href="/A350105/b350105.txt">Table of n, a(n) for n = 0..3305</a>
%F A350105 See the formulas in A350102.
%F A350105 a(n) = 2^n - A350102(n).
%o A350105 (SageMath)
%o A350105 def A350105List(len):
%o A350105     L = [0] * len
%o A350105     b, z = 2, 2
%o A350105     for n in (2..len-1):
%o A350105         b += sloane.A000005(n - 1)
%o A350105         z += z
%o A350105         L[n] = z - b
%o A350105     return L
%o A350105 print(A350105List(35))
%Y A350105 Cf. A350102, A350103, A349976.
%K A350105 nonn
%O A350105 0,4
%A A350105 _Peter Luschny_, Dec 16 2021