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A302941 Number of total dominating sets in the 2n-crossed prism graph. 1
9, 121, 1296, 14161, 154449, 1684804, 18378369, 200477281, 2186871696, 23855111401, 260219353689, 2838557779204, 30963916217529, 337764520613641, 3684445810532496, 40191139395243841, 438418087537149729, 4782407823513403204, 52168067971110285489 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..19.

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).

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)

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]

PROG

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

CROSSREFS

Cf. A006497, A287062, A291772, A302946.

Sequence in context: A017102 A167722 A103930 * A183514 A138978 A046184

Adjacent sequences:  A302938 A302939 A302940 * A302942 A302943 A302944

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Apr 16 2018

EXTENSIONS

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

STATUS

approved

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Last modified March 29 21:32 EDT 2020. Contains 333117 sequences. (Running on oeis4.)