cp's OEIS Frontend

A088808 Number of subsets of {1, ..., n} that are not double-free.

%I A088808 #26 Feb 16 2025 08:32:51
%S A088808 0,0,1,2,6,12,34,68,160,320,736,1472,3136,6272,13504,27008,56176,
%T A088808 112352,234064,468128,954976,1909952,3913504,7827008,15878656,
%U A088808 31757312,64413184,128826368,259449856,518899712,1046785024,2093570048,4207876096,8415752192
%N A088808 Number of subsets of {1, ..., n} that are not double-free.
%C A088808 a(n) = 2^n - A050291(n); a(2*k+1) = a(2*k)*2;
%C A088808 a non-double-free subset contains at least one subset {x,y} with y=2*x.
%H A088808 Alois P. Heinz, <a href="/A088808/b088808.txt">Table of n, a(n) for n = 0..3321</a> (first 401 terms from T. D. Noe)
%H A088808 Steven R. Finch, <a href="/FinchTriple.html">Triple-Free Sets of Integers</a> [From Steven Finch, Apr 20 2019]
%H A088808 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Double-FreeSet.html">Double-Free Set</a>
%H A088808 Reinhard Zumkeller, <a href="/A088808/a088808.txt">Illustration of initial terms</a>
%t A088808 A050291[n_] := A050291[n] = If[n == 1, 2, With[{b = IntegerExponent[2n, 2]}, A050291[n - 1] Fibonacci[b + 2]/Fibonacci[b + 1]]];
%t A088808 a[n_] := If[n == 0, 0, 2^n - A050291[n]];
%t A088808 Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Nov 10 2021 *)
%Y A088808 Cf. A000079, A050291.
%K A088808 nonn
%O A088808 0,4
%A A088808 _Reinhard Zumkeller_, Oct 19 2003