OFFSET
1,2
COMMENTS
1-triangular snake = K_1 has no total dominating sets and so its count (0) differs from a(1) = 1.
LINKS
Eric Weisstein's World of Mathematics, Total Dominating Set
Eric Weisstein's World of Mathematics, Triangular Snake Graph
Index entries for linear recurrences with constant coefficients, signature (2,3,2).
FORMULA
a(n) = 2*a(n-1) + 3*a(n-2) + 2*a(n-3).
G.f.: x*(-1 - 2*x - 5*x^2)/(-1 + 2*x + 3*x^2 + 2*x^3).
MATHEMATICA
Table[RootSum[-2 - 3 # - 2 #^2 + #^3 &, 65 #^n - 100 #^(n + 1) + 31 #^(n + 2) &]/122, {n, 20}]
LinearRecurrence[{2, 3, 2}, {1, 4, 16}, 20]
CoefficientList[Series[(-1 - 2 x - 5 x^2)/(-1 + 2 x + 3 x^2 + 2 x^3), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jun 09 2019
STATUS
approved