A294140 Number of total dominating sets in the n-crown graph.

0, 1, 16, 121, 676, 3249, 14400, 61009, 252004, 1026169, 4145296, 16670889, 66879684, 267944161, 1072693504, 4292739361, 17175150916, 68709515625, 274856935824, 1099467588025, 4397954236900, 17591993106961, 70368341525056, 281474137850481, 1125898162012836

Offset

1,3

Comments

In a total dominating set each side of the crown graph requires any two vertices on the other side to dominate it. - Andrew Howroyd, Apr 16 2018

Links

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Crown Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (11,-47,101,-116,68,-16).

Formula

a(n) = (2^n - 1 - n)^2. - Andrew Howroyd, Apr 16 2018

a(n) = 11*a(n-1) - 47*a(n-2) + 101*a(n-3) - 116*a(n-4) + 68*a(n-5) -16*a(n-6).

G.f.: x^2*(1 + 5*x - 8*x^2 - 4*x^3)/((-1 + x)^3*(-1 + 2*x)^2*(-1 + 4*x)).

Mathematica

Table[(1 - 2^n + n)^2, {n, 20}]
LinearRecurrence[{11, -47, 101, -116, 68, -16}, {0, 1, 16, 121, 676, 3249}, 20]
CoefficientList[Series[x (1 + 5 x - 8 x^2 - 4 x^3)/((-1 + x)^3 (-1 + 2 x)^2 (-1 + 4 x)), {x, 0, 20}], x]

Prog

(PARI) a(n)=(2^n-1-n)^2; \\ Andrew Howroyd, Apr 16 2018

Crossrefs

Cf. A287063, A287471.

Sequence in context: A017030 A082921 A191902 * A014765 A081071 A217022

Adjacent sequences: A294137 A294138 A294139 * A294141 A294142 A294143

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 16 2018

Extensions

a(1)-a(2) and a(11)-a(25) from Andrew Howroyd, Apr 16 2018

Status

approved