A284663 Number of dominating sets in the Moebius ladder M_n.

3, 15, 51, 179, 663, 2439, 8935, 32771, 120219, 440975, 1617531, 5933267, 21763823, 79831879, 292831311, 1074134531, 3940032883, 14452434639, 53012975555, 194456895859, 713287340551, 2616409296967, 9597250953527, 35203676264195, 129130605057163

Offset

1,1

Comments

Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, May 10 2017

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Dominating Set

Eric Weisstein's World of Mathematics, Moebius Ladder

Index entries for linear recurrences with constant coefficients, signature (3,1,5,1,1,-1,-1).

Formula

From Andrew Howroyd, May 10 2017 (Start)

a(n) = 3*a(n-1)+a(n-2)+5*a(n-3)+a(n-4)+a(n-5)-a(n-6)-a(n-7) for n>7.

G.f.: x*(1-x)*(1+x)*(3*x^4+2*x^3+6*x^2+6*x+3)/((x^2+1)*(x^5+x^4-2*x^3 -2*x^2-3*x+1)). (End)

Mathematica

LinearRecurrence[{3, 1, 5, 1, 1, -1, -1}, {3, 15, 51, 179, 663, 2439,
  8935}, 20] (* Eric W. Weisstein, May 17 2017 *)
Rest[CoefficientList[Series[x*(1 - x)*(1 + x)*(3*x^4 + 2*x^3 + 6*x^2 + 6*x + 3)/((x^2 + 1)*(x^5 + x^4 - 2*x^3 - 2*x^2 - 3*x + 1)), {x, 0, 50}], x]] (* G. C. Greubel, May 17 2017 *)
Table[RootSum[1 + # - 2 #^2 - 2 #^3 - 3 #^4 + #^5 &, #^n &] - 2 Cos[n Pi/2], {n, 20}] (* Eric W. Weisstein, Jun 14 2017 *)

Prog

(PARI)
Vec((1-x)*(1+x)*(3*x^4+2*x^3+6*x^2+6*x+3)/((x^2+1)*(x^5+x^4-2*x^3-2*x^2-3*x+1))+O(x^50)) \\ Andrew Howroyd, May 10 2017

Crossrefs

Cf. A182143, A284702, A218348 (ladder).

Sequence in context: A248122 A118126 A282464 * A231747 A192742 A166035

Adjacent sequences: A284660 A284661 A284662 * A284664 A284665 A284666

Keyword

nonn

Author

Eric W. Weisstein, Mar 31 2017

Extensions

a(1)-(2) and a(16)-a(25) from Andrew Howroyd, May 10 2017

Status

approved