OFFSET
1,1
COMMENTS
Number of dominating sets in the n X n X n complete tripartite graph.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Complete Tripartite Graph
Eric Weisstein's World of Mathematics, Dominating Set
Index entries for linear recurrences with constant coefficients, signature (11,-26,16).
FORMULA
a(n) = 8^n - 3*2^n + 5.
a(n) = 11*a(n-1) - 26*a(n-2) + 16*a(n-3).
G.f.: x*(7 - 20*x + 48*x^2)/(1 - 11*x + 26*x^2 - 16*x^3).
E.g.f.: exp(8*x) - 3*exp(2*x) + 5*exp(x) - 3. - G. C. Greubel, Aug 26 2017
MATHEMATICA
Table[8^n - 3 2^n + 5, {n, 20}]
LinearRecurrence[{11, -26, 16}, {7, 57, 493}, 20]
CoefficientList[Series[(-7 + 20 x - 48 x^2)/(-1 + 11 x - 26 x^2 + 16 x^3), {x, 0, 20}], x]
PROG
(PARI) x='x+O('x^50); Vec(x*(7 - 20*x + 48*x^2)/(1 - 11*x + 26*x^2 - 16*x^3)) \\ G. C. Greubel, Aug 26 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 25 2017
STATUS
approved