OFFSET
1,1
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).
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.
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]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Sep 09 2021
STATUS
approved