OFFSET
2,1
COMMENTS
Also the Hosoya indices of the Moebius ladders. - Eric W. Weisstein, Jul 11 2011
LINKS
Colin Barker, Table of n, a(n) for n = 2..1000
J. P. McSorley, Counting structures in the Moebius ladder, Discrete Math., 184 (1998), 137-164.
Eric Weisstein's World of Mathematics, Independent Edge Set
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Moebius Ladder
Index entries for linear recurrences with constant coefficients, signature (2,4,0,-1).
FORMULA
G.f.: 2*x^2*(5+7*x-x^2-2*x^3)/((1+x)*(1-3*x-x^2+x^3)). - Emeric Deutsch, Dec 21 2004
a(n) = 2*a(n-1) + 4*a(n-2) - a(n-4). - Eric W. Weisstein, Oct 03 2017 [Corrected by Altug Alkan, Apr 06 2018]
The McSorley reference gives the approximation a(n)~(3.2143)^n+(-0.6751)^n+(0.4608)^n-(-1)^n. - Emeric Deutsch, Dec 21 2004
MAPLE
G:=2*x^2*(5+7*x-x^2-2*x^3)/(1+x)/(1-3*x-x^2+x^3): Gser:=series(G, x=0, 29): seq(coeff(Gser, x^n), n=2..27); # Emeric Deutsch, Dec 21 2004
MATHEMATICA
Table[RootSum[1 - # - 3 #^2 + #^3 &, #^n &] - (-1)^n, {n, 2, 20}] (* Eric W. Weisstein, Mar 31 2017 *)
LinearRecurrence[{2, 4, 0, -1}, {10, 34, 106, 344}, 20] (* Eric W. Weisstein, Mar 31 2017 *)
CoefficientList[Series[-2 (-5 - 7 x + x^2 + 2 x^3)/(1 - 2 x - 4 x^2 + x^4), {x, 0, 20}], x] (* Eric W. Weisstein, Oct 03 2017 *)
PROG
(PARI) Vec(-2*x^2*(2*x^3+x^2-7*x-5)/((x+1)*(x^3-x^2-3*x+1)) + O(x^50)) \\ Colin Barker, Aug 01 2015
(Magma) I:=[10, 34, 106, 344]; [n le 4 select I[n] else 2*Self(n-1)+4*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Apr 07 2018
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
EXTENSIONS
More terms from Emeric Deutsch, Dec 21 2004
STATUS
approved