A302941 Number of total dominating sets in the 2n-crossed prism graph.

9, 121, 1296, 14161, 154449, 1684804, 18378369, 200477281, 2186871696, 23855111401, 260219353689, 2838557779204, 30963916217529, 337764520613641, 3684445810532496, 40191139395243841, 438418087537149729, 4782407823513403204, 52168067971110285489

Offset: 1

Author

Eric W. Weisstein, Apr 16 2018

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Crossed Prism Graph
• Eric Weisstein's World of Mathematics, Total Dominating Set
• Index entries for linear recurrences with constant coefficients, signature (10,10,-1).

Crossrefs

Cf. A006497, A287062, A291772, A302946.

Programs

Mathematica

Table[2 (-1)^n + ((11 - 3 Sqrt[13])/2)^n + ((11 + 3 Sqrt[13])/2)^n, {n, 20}] // FullSimplify
Table[LucasL[n, 3]^2, {n, 20}]
LucasL[Range[20], 3]^2
LinearRecurrence[{10, 10, -1}, {9, 121, 1296}, 20]
CoefficientList[Series[(9 + 31 x - 4 x^2)/(1 - 10 x - 10 x^2 + x^3), {x, 0, 20}], x]

PARI

Vec((9 + 31*x - 4*x^2)/((1 + x)*(1 - 11*x + x^2)) + O(x^30)) \\ Andrew Howroyd, Apr 16 2018

Formula

From Andrew Howroyd, Apr 16 2018: (Start)

G.f.: x*(9 + 31*x - 4*x^2)/((1 + x)*(1 - 11*x + x^2)).

a(n) = 10*a(n-1) + 10*a(n-2) - a(n-3) for n > 3.

a(n) = A006497(n)^2. (End)

Extensions

a(1) and terms a(6) and beyond from Andrew Howroyd, Apr 16 2018