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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
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Crossed Prism Graph
Eric Weisstein's World of Mathematics, Total Dominating Set
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
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