OFFSET
1,1
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).
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