Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #19 Jan 27 2022 17:23:12
%S 2,18,194,2130,23426,257682,2834498,31179474,342974210,3772716306,
%T 41499879362,456498672978,5021485402754,55236339430290,
%U 607599733733186,6683597071065042,73519567781715458,808715245598870034,8895867701587570370,97854544717463274066
%N Expansion of (2-6*x)/(1-12*x+11*x^2).
%H Harvey P. Dale, <a href="/A156341/b156341.txt">Table of n, a(n) for n = 0..960</a>
%H Tomislav Došlić and Frode Måløy, <a href="http://dx.doi.org/10.1016/j.disc.2009.11.026">Chain hexagonal cacti: Matchings and independent sets</a>, Discr. Math., 310 (2010), 1676-1690.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-11).
%F From _Felix P. Muga II_, Mar 19 2014: (Start)
%F a(n) = 12*a(n-1)-11*a(n-2) for n>=2, a(0)=2, a(1)=18.
%F a(n) = a(n-1)+16*11^(n-1) for n >=1, a(0)=2.
%F a(n) = 10*a(n-1)+11*a(n-2)-8 for n>=2, a(0)=2, a(1)=18.
%F a(n) = (8/5)*11^n + 2/5. (End)
%t CoefficientList[Series[(2-6x)/(1-12x+11x^2),{x,0,40}],x] (* or *) LinearRecurrence[{12,-11},{2,18},40] (* _Harvey P. Dale_, Jan 27 2022 *)
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, May 22 2010