A308591 Number of minimal total dominating sets in the (2n-1)-triangular snake graph.

0, 3, 5, 7, 14, 22, 42, 70, 127, 218, 388, 675, 1191, 2083, 3663, 6420, 11275, 19777, 34716, 60912, 106904, 187592, 329213, 577716, 1013834, 1779141, 3122189, 5479045, 9615069, 16873254, 29610513, 51962811, 91188394, 160024458, 280823366, 492810634, 864822395

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Minimal Total Dominating Set.

Eric Weisstein's World of Mathematics, Triangular Snake Graph.

Index entries for linear recurrences with constant coefficients, signature (0,2,1,1,1).

Formula

From Andrew Howroyd, Sep 08 2019: (Start)

a(n) = 2*a(n-2) + a(n-3) + a(n-4) + a(n-5) for n > 7.

G.f.: x^2*(3 + 5*x + x^2 + x^3 - x^5)/((1 + x)^2*(1 - 2*x + x^2 - x^3)).

(End)

Mathematica

Join[{0, 3}, Table[((3 - 5 n) (-1)^n + RootSum[-1 + # - 2 #^2 + #^3 &, -2 #^n + 249 #^(n + 1) + 7 #^(n + 2) &]/23)/25, {n, 3, 20}]] (* Eric W. Weisstein, Sep 19 2021 *)
Join[{0, 3}, LinearRecurrence[{0, 2, 1, 1, 1}, {5, 7, 14, 22, 42}, 20]] (* Eric W. Weisstein, Sep 19 2021 *)
CoefficientList[Series[x (-3 - 5 x - x^2 - x^3 + x^5)/((1 + x)^2 (-1 + 2 x - x^2 + x^3)), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 19 2021 *)

Prog

(PARI) concat([0], Vec((3 + 5*x + x^2 + x^3 - x^5)/((1 + x)^2*(1 - 2*x + x^2 - x^3)) + O(x^40))) \\ Andrew Howroyd, Sep 08 2019

Crossrefs

Cf. A308592.

Sequence in context: A376532 A024372 A295717 * A309832 A319784 A346503

Adjacent sequences: A308588 A308589 A308590 * A308592 A308593 A308594

Keyword

nonn,easy,changed

Author

Eric W. Weisstein, Jun 09 2019

Extensions

Terms a(11) and beyond from Andrew Howroyd, Sep 08 2019

Status

approved