login
A286879
Number of minimal dominating sets in the n-Andrásfai graph.
3
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
Eric Weisstein's World of Mathematics, Andrásfai Graph
Eric Weisstein's World of Mathematics, Minimal Dominating Set
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
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