A347551 Number of minimum dominating sets in the 2n-crossed prism graph.

4, 51, 8, 170, 16, 476, 32, 1224, 64, 2992, 128, 7072, 256, 16320, 512, 36992, 1024, 82688, 2048, 182784, 4096, 400384, 8192, 870400, 16384, 1880064, 32768, 4038656, 65536, 8634368, 131072, 18382848, 262144, 38993920, 524288, 82444288, 1048576, 173801472

Offset: 2

Author

Eric W. Weisstein, Sep 06 2021

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..1000
• Eric Weisstein's World of Mathematics, Crossed Prism Graph
• Eric Weisstein's World of Mathematics, Minimum Dominating Set
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-4).

Crossrefs

Cf. A287062, A291772, A302946.

Programs

Mathematica

Table[Piecewise[{{17 n 2^((n - 3)/2), Mod[n, 2] == 1}, {2^((n/2) + 1), Mod[n, 2] == 0}}], {n, 2, 20}] (* Eric W. Weisstein, Feb 27 2025 *)
CoefficientList[Series[(4 + 51 x - 8 x^2 - 34 x^3)/(1 - 2 x^2)^2, {x, 0, 20}], x] (* Eric W. Weisstein, Feb 27 2025 *)

PARI

a(n) = if(n%2, 17*n*2^((n-3)/2), 2^((n/2)+1)) \\ Andrew Howroyd, Jan 18 2022

Formula

a(n) = 2^((n/2)+1) for n even.

From Andrew Howroyd, Jan 18 2022: (Start)

a(n) = 17*n*2^((n-3)/2) for n odd.

a(n) = 4*a(n-2) - 4*a(n-4) for n > 5.

G.f.: x^2*(4 + 51*x - 8*x^2 - 34*x^3)/(1 - 2*x^2)^2.

(End)

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 18 2022