login
A288795
a(n) = 4^n + 3^(n + 1) - 2.
1
11, 41, 143, 497, 1751, 6281, 22943, 85217, 321191, 1225721, 4725743, 18371537, 71891831, 282784361, 1116788543, 4424107457, 17567289671, 69881738201, 278364691343, 1109971980977, 4429427570711, 17686329223241, 70651173714143, 282322265320097, 1128441772670951
OFFSET
1,1
COMMENTS
Number of dominating sets in the n-book graph.
LINKS
Eric Weisstein's World of Mathematics, Book Graph
Eric Weisstein's World of Mathematics, Dominating Set
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
Sequence in context: A268930 A139933 A243892 * A213659 A199209 A156733
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 29 2017
STATUS
approved