A286879 Number of minimal dominating sets in the n-Andrásfai graph.

2, 5, 28, 66, 140, 272, 489, 828, 1339, 2088, 3160, 4662, 6726, 9512, 13211, 18048, 24285, 32224, 42210, 54634, 69936, 88608, 111197, 138308, 170607, 208824, 253756, 306270, 367306, 437880, 519087, 612104, 718193, 838704, 975078, 1128850, 1301652, 1495216, 1711377

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Andrásfai Graph

Eric Weisstein's World of Mathematics, Minimal Dominating Set

Index entries for linear recurrences with constant coefficients, signature (6,-15, 20,-15,6,-1).

Formula

From Eric W. Weisstein, Aug 21 2017: (Start)

a(n) = (3*n - 1)*(n^4 - 13*n^3 + 164*n^2 - 572*n + 960)/120 for n > 3.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 9.

G.f.: (x (2 - 7 x + 28 x^2 - 67 x^3 + 94 x^4 - 75 x^5 + 29 x^6 + x^7 - 2 x^8))/(-1 + x)^6.

(End)

Maple

A286879:=n->(3*n - 1)*(n^4 - 13*n^3 + 164*n^2 - 572*n + 960)/120: 2, 5, 28, seq(A286879(n), n=4..100); # Wesley Ivan Hurt, Nov 30 2017

Mathematica

Table[Piecewise[{{2, n == 1}, {5, n == 2}, {28, n == 3}}, (3 n - 1) (n^4 - 13 n^3 + 164 n^2 - 572 n + 960)/120], {n, 20}]
Join[{2, 5, 28}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {66, 140, 272, 489, 828, 1339}, 20]] (* Eric W. Weisstein, Aug 21 2017 *)
CoefficientList[Series[(2 - 7 x + 28 x^2 - 67 x^3 + 94 x^4 - 75 x^5 + 29 x^6 + x^7 - 2 x^8)/(-1 + x)^6, {x, 0, 20}], x] (* Eric W. Weisstein, Aug 21 2017 *)

Prog

(Magma) [2, 5, 28] cat [(3*n-1)*(n^4-13*n^3+164*n^2-572*n+ 960)/120: n in [4..40]]; // Vincenzo Librandi, Sep 03 2017

Crossrefs

Cf. A285272, A290587, A291053.

Sequence in context: A127357 A025170 A151775 * A326230 A095159 A047132

Adjacent sequences: A286876 A286877 A286878 * A286880 A286881 A286882

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 02 2017

Extensions

a(10)-a(20) from Andrew Howroyd, Aug 19 2017

a(21) and higher from Eric W. Weisstein, Aug 21 2017

Status

approved