OFFSET
0,1
REFERENCES
J. P. McSorley, Counting structures in the Moebius ladder, Discrete Math., 184 (1998), 137-164.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Maximum Independent Edge Set
Eric Weisstein's World of Mathematics, Moebius Ladder
Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-1).
FORMULA
If n mod 2 = 0 then L(n) else L(n)+2, where L() are the Lucas numbers.
a(n) = A001350(n) + 2.
G.f.: (2 + x - 4*x^2 - x^3) / ((1 - x)*(1 + x)*(1 - x - x^2)). - Colin Barker, Jan 23 2012
From Colin Barker, Jul 12 2017: (Start)
a(n) = ((1 - sqrt(5))/2)^n + ((1 + sqrt(5))/2)^n for n even.
a(n) = ((1 - sqrt(5))/2)^n + ((1 + sqrt(5))/2)^n + 2 for n odd.
a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n>3.
(End)
MATHEMATICA
CoefficientList[Series[(2+x-4*x^2-x^3)/((1+x)*(1-x)*(1-x-x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 20 2012 *)
Table[1 - (-1)^n + LucasL[n], {n, 20}] (* Eric W. Weisstein, Dec 31 2017 *)
LinearRecurrence[{1, 2, -1, -1}, {3, 3, 6, 7}, 20] (* Eric W. Weisstein, Dec 31 2017 *)
PROG
(Magma) I:=[2, 3, 3, 6]; [n le 4 select I[n] else Self(n-1)+2*Self(n-2)-Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Apr 20 2012
(PARI) Vec((2 + x - 4*x^2 - x^3) / ((1 - x)*(1 + x)*(1 - x - x^2)) + O(x^50)) \\ Colin Barker, Jul 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved