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

2,1

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).

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)

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 *)

Prog

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

Crossrefs

Cf. A287062, A291772, A302946.

Sequence in context: A221477 A122464 A226375 * A048995 A215639 A320645

Adjacent sequences: A347548 A347549 A347550 * A347552 A347553 A347554

Keyword

nonn,changed

Author

Eric W. Weisstein, Sep 06 2021

Extensions

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

Status

approved