A287430 Number of connected dominating sets in the 2n-crossed prism graph.

115, 1063, 9121, 75607, 611569, 4857223, 38034241, 294475447, 2258978449, 17196401383, 130059675361, 978211787287, 7322040929329, 54576195433543, 405286730532481, 2999780651211127, 22137879320864209, 162941058582753703, 1196418733436205601

Offset

2,1

Links

Andrew Howroyd, Table of n, a(n) for n = 2..200

Eric Weisstein's World of Mathematics, Connected Dominating Set

Eric Weisstein's World of Mathematics, Crossed Prism Graph

Index entries for linear recurrences with constant coefficients, signature (14, -49).

Formula

From Andrew Howroyd, Sep 05 2017: (Start)

a(n) = 7^n + 240*n*7^(n-3) for n > 2.

a(n) = 14*a(n-1) - 49*a(n-2) for n > 4.

G.f.: x^2*(115 - 547*x - 126*x^2)/(1 - 7*x)^2.

(End)

Mathematica

Join[{115}, Table[7^(n - 3) (343 + 240 n), {n, 3, 20}]]
LinearRecurrence[{14, -49}, {115, 1063, 9121}, 19] (* amended by Georg Fischer, Apr 03 2019 *)
CoefficientList[Series[(115 - 547 x - 126 x^2)/(-1 + 7 x)^2, {x, 0, 20}], x]

Prog

(PARI) Vec((115 - 547*x - 126*x^2)/(1 - 7*x)^2 + O(x^20)) \\ Andrew Howroyd, Sep 05 2017

Crossrefs

Cf. A287062, A290757.

Sequence in context: A251215 A218324 A258673 * A256889 A256354 A005466

Adjacent sequences: A287427 A287428 A287429 * A287431 A287432 A287433

Keyword

nonn

Author

Eric W. Weisstein, May 25 2017

Extensions

Terms a(6) and beyond from Andrew Howroyd, Sep 05 2017

Status

approved