A286879 -id:A286879 - cp's OEIS frontend

A285272 Number of dominating sets in the n-Andrásfai graph.

3, 21, 179, 1607, 14087, 119749, 994775, 8139609, 65978747, 531817661, 4272634559, 34261960897, 274453098179, 2197189450437

Offset: 1

Eric W. Weisstein, Jun 14 2017

Eric Weisstein's World of Mathematics, Andrásfai Graph
Eric Weisstein's World of Mathematics, Dominating Set

Cf. A286879, A287429, A302759.

a(11)-a(14) from Andrew Howroyd, Apr 18 2018

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

A285272 Number of dominating sets in the n-Andrásfai graph.

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