A266550 Independence number, upper domination number, and upper irredundance number of the n-Mycielski graph.

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

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Independence Number.

Eric Weisstein's World of Mathematics, Mycielski Graph.

Eric Weisstein's World of Mathematics, Upper Domination Number.

Eric Weisstein's World of Mathematics, Upper Irredundance Number.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

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

Cf. A052940, A055010, A083329, A153893.

Sequence in context: A153893 A083329 A055010 * A081973 A357292 A334276

Adjacent sequences: A266547 A266548 A266549 * A266551 A266552 A266553

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 31 2015

Extensions

Definition broadened by Eric W. Weisstein, Feb 23 2026

Status

approved