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A266550
Independence number of the n-Mycielski graph.
3
1, 1, 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, 3145727, 6291455, 12582911, 25165823, 50331647, 100663295, 201326591, 402653183, 805306367, 1610612735, 3221225471, 6442450943, 12884901887
OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Independence Number.
Eric Weisstein's World of Mathematics, Mycielski Graph.
FORMULA
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).
G.f.: x + x^2*(1 - x + x^2)/((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1)-2*a(n-2) for n>2. - Vincenzo Librandi, Jan 01 2016
a(n) = A052940(n-3) for n > 3. - Georg Fischer, Oct 23 2018
E.g.f.: (3*exp(2*x) - 8*exp(x) + 5 + 10*x+ 2*x^2)/8. - Stefano Spezia, Sep 14 2024
MATHEMATICA
Table[Piecewise[{{-1 + 3 2^(n - 3), n > 2}}, 1], {n, 35}]
CoefficientList[Series[1 + x*(1 - x + x^2)/((1 - x)*(1 - 2*x)), {x, 0, 35}], x] (* Vincenzo Librandi, Jan 01 2016 *)
PROG
(Magma) [1, 1] cat [-1+3*2^(n-3): n in [3..40]]; // Vincenzo Librandi, Jan 01 2016
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Dec 31 2015
STATUS
approved