A308592 Number of total dominating sets in the (2n-1)-triangular snake (for n > 1).

1, 4, 16, 46, 148, 466, 1468, 4630, 14596, 46018, 145084, 457414, 1442116, 4546642, 14334460, 45193078, 142482820, 449213794, 1416262204, 4465131430, 14077477060, 44382872818, 139928439676, 441160451926, 1390871968516, 4385082172162, 13825101153724

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

Table of n, a(n) for n=1..27.

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

Sequence in context: A174836 A244252 A369401 * A050616 A297160 A006009

Adjacent sequences: A308589 A308590 A308591 * A308593 A308594 A308595

Keyword

nonn

Author

Eric W. Weisstein, Jun 09 2019

Status

approved