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

Author

Eric W. Weisstein, May 25 2017

Keywords

• nonn

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).

Crossrefs

Cf. A287062, A290757.

Programs

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]

PARI

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

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)

Extensions

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