A284702 Number of dominating sets in the n-prism graph.

3, 11, 51, 183, 663, 2435, 8935, 32775, 120219, 440971, 1617531, 5933271, 21763823, 79831875, 292831311, 1074134535, 3940032883, 14452434635, 53012975555, 194456895863, 713287340551, 2616409296963, 9597250953527, 35203676264199, 129130605057163

Offset

1,1

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000 (terms 1..200 from Andrew Howroyd)

Eric Weisstein's World of Mathematics, Dominating Set

Eric Weisstein's World of Mathematics, Prism Graph

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).

G.f.: x*(-7*x^6 - 6*x^5 + 5*x^4 + 4*x^3 + 15*x^2 + 2*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, 11, 51, 183, 663, 2435,
  8935}, 20] (* Eric W. Weisstein, May 17 2017 *)
Rest[CoefficientList[Series[x (-7 x^6 - 6 x^5 + 5 x^4 + 4 x^3 + 15 x^2 + 2 x + 3)/((x^2 + 1) (x^5 + x^4 - 2 x^3 - 2 x^2 - 3 x + 1)), {x, 0, 20}], x]] (* G. C. Greubel, May 17 2017 *)
Table[2 Cos[n Pi/2] + RootSum[1 + #1 - 2 #1^2 - 2 #1^3 - 3 #1^4 + #1^5 &, #^n &], {n, 20}] (* Eric W. Weisstein, May 26 2017 *)

Prog

(PARI)
Vec((-7*x^6-6*x^5+5*x^4+4*x^3+15*x^2+2*x+3)/((x^2+1)*(x^5+x^4-2*x^3-2*x^2-3*x+1))+O(x^15)) \\ Andrew Howroyd, May 10 2017

Crossrefs

Cf. A051927, A102080, A284699, A218348 (ladder), A284663.

Sequence in context: A024336 A145144 A367560 * A191341 A359146 A199212

Adjacent sequences: A284699 A284700 A284701 * A284703 A284704 A284705

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 01 2017

Extensions

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

Status

approved