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A266550 Independence number of the n-Mycielski graph.

%I A266550 #31 Feb 16 2025 08:33:28
%S A266550 1,1,2,5,11,23,47,95,191,383,767,1535,3071,6143,12287,24575,49151,
%T A266550 98303,196607,393215,786431,1572863,3145727,6291455,12582911,25165823,
%U A266550 50331647,100663295,201326591,402653183,805306367,1610612735,3221225471,6442450943,12884901887
%N A266550 Independence number of the n-Mycielski graph.
%H A266550 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependenceNumber.html">Independence Number</a>.
%H A266550 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MycielskiGraph.html">Mycielski Graph</a>.
%H A266550 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A266550 a(1) = 1, a(2) = 1; for n>2, a(n) = -1 + 3*2^(n-3) = A083329(n-2) = A055010(n-2) = A153893(n-3).
%F A266550 G.f.: x + x^2*(1 - x + x^2)/((1 - x)*(1 - 2*x)).
%F A266550 a(n) = 3*a(n-1)-2*a(n-2) for n>2. - _Vincenzo Librandi_, Jan 01 2016
%F A266550 a(n) = A052940(n-3) for n > 3. - _Georg Fischer_, Oct 23 2018
%F A266550 E.g.f.: (3*exp(2*x) - 8*exp(x) + 5 + 10*x+ 2*x^2)/8. - _Stefano Spezia_, Sep 14 2024
%t A266550 Table[Piecewise[{{-1 + 3 2^(n - 3), n > 2}}, 1], {n, 35}]
%t A266550 CoefficientList[Series[1 + x*(1 - x + x^2)/((1 - x)*(1 - 2*x)), {x, 0, 35}], x] (* _Vincenzo Librandi_, Jan 01 2016 *)
%o A266550 (Magma) [1,1] cat [-1+3*2^(n-3): n in [3..40]]; // _Vincenzo Librandi_, Jan 01 2016
%o A266550 (Magma) I:=[1,1,2,5]; [n le 4 select I[n] else 3*Self(n-1)-2*Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Jan 01 2016
%Y A266550 Cf. A052940, A055010, A083329, A153893.
%K A266550 nonn,easy
%O A266550 1,3
%A A266550 _Eric W. Weisstein_, Dec 31 2015