%I #24 Oct 05 2017 13:53:55
%S 0,3,4,11,17,36,69,133,254,499,959,1852,3589,6943,13410,25951,50197,
%T 97050,187699,363047,702066,1357755,2625947,5078438,9821417,18994465,
%U 36734648,71043261,137395463,265718350,513889567,993844901,1922062694,3717202293,7188941039
%N Number of maximal 2-independent sets in the planar 3 X n grid graph.
%H Andrew Howroyd, <a href="/A231882/b231882.txt">Table of n, a(n) for n = 0..200</a>
%H R. Euler, P. Oleksik, Z. Skupien, <a href="http://dx.doi.org/10.7151/dmgt.1707">Counting Maximal Distance-Independent Sets in Grid Graphs</a>, Discussiones Mathematicae Graph Theory. Volume 33, Issue 3, Pages 531-557, ISSN (Print) 2083-5892, July 2013; see <a href="http://www.degruyter.com/view/j/dmgt.2013.33.issue-3/dmgt.1707/dmgt.1707.xml">also</a>.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,3,1,0,1,-2,0,-1).
%F Euler et al. give an explicit g.f. and recurrence.
%F G.f.: x*(3 + x + 7*x^2 - 3*x^3 + 4*x^4 - 4*x^5 - x^6 - 2*x^7 - x^8) / ((1 + x)*(1 - 2*x + 2*x^2 - 5*x^3 + 4*x^4 - 4*x^5 + 3*x^6 - x^7 + x^8)). - _Colin Barker_, Oct 03 2017
%t LinearRecurrence[{1,0,3,1,0,1,-2,0,-1},{0,3,4,11,17,36,69,133,254,499},40] (* _Harvey P. Dale_, Oct 05 2017 *)
%Y Cf. A197054, A197049.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Nov 17 2013
%E Terms a(10) and beyond from _Andrew Howroyd_, Jun 10 2017