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A231884 Number of maximal 2-independent sets in the 3-dimensional (2, 2, n) grid graph.

%I A231884 #29 Nov 01 2017 18:30:32
%S A231884 0,4,4,20,32,80,180,408,940,2072,4824,10792,24660,55748,126760,287584,
%T A231884 652280,1481184,3359900,7627296,17305472,39277688,89131928,202276640,
%U A231884 459045772,1041743020,2364140452,5365103100,12175556108,27630957644,62705400664,142302685268
%N A231884 Number of maximal 2-independent sets in the 3-dimensional (2, 2, n) grid graph.
%H A231884 Andrew Howroyd, <a href="/A231884/b231884.txt">Table of n, a(n) for n = 0..200</a>
%H A231884 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 A231884 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,4,4,0,-9,-3).
%F A231884 Euler et al. give an explicit g.f. and recurrence.
%F A231884 From _Colin Barker_, Oct 04 2017: (Start)
%F A231884 G.f.: 4*x*(1 + x)*(1 + 2*x^2 - x^3 - 2*x^4 - x^5) / (1 - 3*x^2 - 4*x^3 - 4*x^4 + 9*x^6 + 3*x^7).
%F A231884 a(n) = 3*a(n-2) + 4*a(n-3) + 4*a(n-4) - 9*a(n-6) - 3*a(n-7) for n>7.
%F A231884 (End)
%t A231884 Join[{0}, LinearRecurrence[{0, 3, 4, 4, 0, -9, -3}, {4, 4, 20, 32, 80, 180, 408}, 31]] (* _Jean-François Alcover_, Nov 01 2017 *)
%o A231884 (PARI) concat(0, Vec(4*x*(1 + x)*(1 + 2*x^2 - x^3 - 2*x^4 - x^5) / (1 - 3*x^2 - 4*x^3 - 4*x^4 + 9*x^6 + 3*x^7) + O(x^40))) \\ _Colin Barker_, Oct 04 2017
%Y A231884 Cf. A197054, A231886, A231887, A231888, A217631, A217632.
%K A231884 nonn,easy
%O A231884 0,2
%A A231884 _N. J. A. Sloane_, Nov 17 2013
%E A231884 Terms a(11) and beyond from _Andrew Howroyd_, Jun 10 2017