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 #22 Jul 11 2023 15:18:49
%S 1,3,9,29,93,299,961,3089,9929,31915,102585,329741,1059893,3406835,
%T 10950657,35198913,113140561,363669939,1168951465,3757383773,
%U 12077432845,38820730843,124782241601,401090022801,1289231579161,4144002518683,13320149112409
%N Expansion of (1-x^2)/(1-3*x-x^2+x^3).
%C The number of tilings of a 2*n grid using dominoes and singletons with two horizontal dominoes or one vertical domino in the two rightmost squares. - _John M. Campbell_, Mar 05 2011
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1056">Encyclopedia of Combinatorial Structures 1056</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-1).
%F a(n) = 3*a(n-1)+a(n-2)-a(n-3) for n>3. - _Colin Barker_, Sep 13 2014
%F G.f.: -(x-1)*(x+1) / (x^3-x^2-3*x+1). - _Colin Barker_, Sep 13 2014
%F a(n) = A033505(n)-A033505(n-2). - _R. J. Mathar_, Oct 24 2015
%o (PARI) Vec(-(x-1)*(x+1)/(x^3-x^2-3*x+1) + O(x^100)) \\ _Colin Barker_, Sep 13 2014
%Y Cf. A033505.
%K nonn,easy
%O 0,2
%A _Henry Bottomley_, May 16 2001