A347634 Number of minimum dominating sets in the n-prism graph (for n > 3 except n = 6).

2, 8, 6, 4, 10, 48, 14, 4, 18, 120, 22, 4, 26, 224, 30, 4, 34, 360, 38, 4, 42, 528, 46, 4, 50, 728, 54, 4, 58, 960, 62, 4, 66, 1224, 70, 4, 74, 1520, 78, 4, 82, 1848, 86, 4, 90, 2208, 94, 4, 98, 2600, 102, 4, 106, 3024, 110, 4, 114, 3480, 118, 4, 122, 3968

Offset: 1

Author

Eric W. Weisstein, Sep 09 2021

Keywords

• nonn

Comments

The numbers of minimum dominating sets in the n-prism graph differ at n = 3 (9 minimum sets) and n = 6 (51 minimum sets).

Links

• Eric Weisstein's World of Mathematics, Minimum Dominating Set
• Eric Weisstein's World of Mathematics, Prism Graph
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

Programs

Mathematica

Table[Piecewise[{{4, Mod[n, 4] == 0}, {2 n, Mod[n, 2] == 1}, {n (n + 2), Mod[n, 4] == 2}}], {n, 20}]
LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {2, 8, 6, 4, 10, 48, 14, 4, 18, 120, 22, 4}, 20]

Formula

a(n) = 4 for n = 0 (mod 4)

2*n for n = 1 (mod 2)

n*(n+2) for n = 2 (mod 4).

a(n) = 3*a(n-4)-3*a(n-8)+a(n-12) for n > 12.