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

Author

Eric W. Weisstein, Apr 16 2018

Keywords

• nonn
• easy

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

• 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).

Crossrefs

Cf. A287063, A287471.

Programs

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]

PARI

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

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)).

Extensions

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