OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Connected Dominating Set
Eric Weisstein's World of Mathematics, Moebius Ladder
Index entries for linear recurrences with constant coefficients, signature (6,-11,4,5,-2,-1).
FORMULA
a(n) = (1 - 5*n)*LucasL(n, 2) + 2*(8*Fibonacci(n, 2) + 1)*n - 1.
a(n) = 6*a(n-1) - 11*a(n-2) + 4*a(n-3) + 5*a(n-4) - 2*a(n-5) - a(n-6).
G.f.: -x*(-9+41*x-70*x^2+58*x^3-29*x^4+x^5)/((-1+x)^2*(-1+2*x+x^2)^2).
MATHEMATICA
Table[(1 - 5 n) LucasL[n, 2] + 2 (8 Fibonacci[n, 2] + 1) n - 1, {n, 20}]
Table[-1 + (1 - Sqrt[2])^n + (1 + Sqrt[2])^n + (2 + (1 + Sqrt[2])^n (-5 + 4 Sqrt[2]) - (1 - Sqrt[2])^n (5 + 4 Sqrt[2])) n, {n, 20}] // Expand
CoefficientList[Series[-((-9 + 41 x - 70 x^2 + 58 x^3 - 29 x^4 + x^5)/((-1 + x)^2 (-1 + 2 x + x^2)^2)), {x, 0, 20}], x]
LinearRecurrence[{6, -11, 4, 5, -2, -1}, {9, 13, 49, 129, 361, 989}, 20]
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, May 17 2017
EXTENSIONS
a(13) from Eric W. Weisstein, Jun 30 2017
a(1), a(2) and a(14) and above from Eric W. Weisstein, Dec 02 2022
STATUS
approved