A291053 -id:A291053 - cp's OEIS frontend

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

Eric W. Weisstein, Aug 02 2017

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).

Cf. A285272, A290587, A291053.

[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

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

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 *)

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)

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

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

A290587 Number of irredundant sets in the n-Andrásfai graph.

Original entry on oeis.org

3, 16, 81, 265, 729, 1786, 4060, 8833, 18786, 39586, 83273, 175463, 370615, 784290, 1661122, 3517669, 7441936, 15720066, 33145015, 69744491, 146458013, 306933394, 642004440, 1340415817, 2793811726, 5813791138, 12080174037, 25065845455, 51943066643, 107509343618, 222265656670, 459025904205, 947041760092, 1952064327682

Offset: 1

Eric W. Weisstein, Aug 07 2017

nonn

Eric Weisstein's World of Mathematics, Andrásfai Graph
Eric Weisstein's World of Mathematics, Irredundant Set
Index entries for linear recurrences with constant coefficients, signature (10, -43, 104, -155, 146, -85, 28, -4).

Cf. A285272, A286879, A291053.

Table[Piecewise[{{3, n == 1}, {16, n == 2}, {81, n == 3}}, (-45 (8 + 3 2^n) + (1772 + 405 2^n) n - 1010 n^2 + 25 n^3 + 50 n^4 + 3 n^5)/120], {n, 20}] (* Eric W. Weisstein, Aug 21 2017 *)
Join[{3, 16, 81}, LinearRecurrence[{10, -43, 104, -155, 146, -85, 28, -4}, {265, 729, 1786, 4060, 8833, 18786, 39586, 83273}, 20]] (* Eric W. Weisstein, Aug 21 2017 *)
CoefficientList[Series[-((-3 + 14 x - 50 x^2 + 169 x^3 - 363 x^4 + 491 x^5 - 461 x^6 + 260 x^7 - 46 x^8 - 22 x^9 + 8 x^10)/((-1 + x)^6 (-1 + 2 x)^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 21 2017 *)

From Eric W. Weisstein, Aug 21 2017: (Start)
a(n) = (-45*(8 + 3*2^n) + (1772 + 405*2^n) n - 1010*n^2 + 25*n^3 + 50*n^4 + 3*n^5)/120 for n > 3.
a(n) = 10*a(n-1) - 43*a(n-2) + 104*a(n-3) - 155*a(n-4) + 146*a(n-5) - 85*a(n-6) + 28*a(n-7) - 4*a(n-8) for n > 11.
G.f.: -((x (-3 + 14 x - 50 x^2 + 169 x^3 - 363 x^4 + 491 x^5 - 461 x^6 + 260 x^7 - 46 x^8 - 22 x^9 + 8 x^10))/((-1 + x)^6 (-1 + 2 x)^2)).
(End)

a(9)-a(20) from Andrew Howroyd, Aug 19 2017

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

cp's OEIS Frontend

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

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