A286879 - OEIS

%I #35 Feb 09 2024 03:04:52

%S 2,5,28,66,140,272,489,828,1339,2088,3160,4662,6726,9512,13211,18048,

%T 24285,32224,42210,54634,69936,88608,111197,138308,170607,208824,

%U 253756,306270,367306,437880,519087,612104,718193,838704,975078,1128850,1301652,1495216,1711377

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

%H Vincenzo Librandi, <a href="/A286879/b286879.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AndrasfaiGraph.html">Andrásfai Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalDominatingSet.html">Minimal Dominating Set</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15, 20,-15,6,-1).

%F From _Eric W. Weisstein_, Aug 21 2017: (Start)

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

%F 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.

%F 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.

%F (End)

%p 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

%t 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}]

%t Join[{2, 5, 28}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {66, 140, 272, 489, 828, 1339}, 20]] (* _Eric W. Weisstein_, Aug 21 2017 *)

%t 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 *)

%o (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

%Y Cf. A285272, A290587, A291053.

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Aug 02 2017

%E a(10)-a(20) from _Andrew Howroyd_, Aug 19 2017

%E a(21) and higher from _Eric W. Weisstein_, Aug 21 2017