OFFSET
1,1
COMMENTS
Number of dominating sets in the n-book graph.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Book Graph
Eric Weisstein's World of Mathematics, Dominating Set
Index entries for linear recurrences with constant coefficients, signature (8,-19,12).
FORMULA
a(n) = 4^n + 3^(n + 1) - 2.
a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3).
G.f.: -((x*(11 - 47*x + 24*x^2))/((-1 + x)*(-1 + 3*x)*(-1 + 4*x))).
MATHEMATICA
Table[4^n + 3^(n + 1) - 2, {n, 20}]
LinearRecurrence[{8, -19, 12}, {11, 41, 143}, 20]
CoefficientList[Series[-((11 - 47 x + 24 x^2)/((-1 + x) (-1 + 3 x) (-1 + 4 x))), {x, 0, 20}], x]
PROG
(Magma) [4^n+3^(n+1)-2: n in [1..30]]; // Vincenzo Librandi, Jun 30 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 29 2017
STATUS
approved