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A218348 Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX2 array.

%I A218348 #22 Feb 16 2025 08:33:18
%S A218348 3,11,41,149,547,2007,7361,27001,99043,363299,1332617,4888173,
%T A218348 17930307,65770159,241251521,884934705,3246028995,11906758971,
%U A218348 43675182633,160204937605,587647732323,2155550649479,7906775346689,29002842683433
%N A218348 Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX2 array.
%C A218348 Number of dominating sets in the ladder graph P_2 X P_n. - _Andrew Howroyd_, May 10 2017
%H A218348 R. H. Hardin, <a href="/A218348/b218348.txt">Table of n, a(n) for n = 1..210</a>
%H A218348 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominatingSet.html">Dominating Set</a>
%H A218348 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LadderGraph.html">Ladder Graph</a>
%H A218348 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,2,2,-1,-1).
%F A218348 a(n) = 3*a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) -a(n-5).
%F A218348 G.f.: x*(3 + 2*x + 2*x^2 - 2*x^3 - x^4)/(1 - 3*x - 2*x^2 - 2*x^3 + x^4 + x^5). - _Andrew Howroyd_, May 10 2017
%e A218348 Some solutions for n=3
%e A218348 ..1..0....1..1....0..1....1..0....1..1....1..1....0..1....0..0....1..0....0..1
%e A218348 ..1..0....0..0....1..1....1..0....0..1....1..1....0..1....1..1....0..0....0..0
%e A218348 ..0..1....1..1....0..1....1..0....1..0....1..0....1..0....0..0....0..1....1..0
%t A218348 LinearRecurrence[{3, 2, 2, -1, -1}, {3, 11, 41, 149, 547}, 20]  (* _Eric W. Weisstein_, Jun 14 2017 *)
%t A218348 CoefficientList[Series[(x (3 + 2 x + 2 x^2 - 2 x^3 - x^4))/(1 - 3 x - 2 x^2 - 2 x^3 + x^4 + x^5), {x, 0, 20}], x] (* _Eric W. Weisstein_, Jun 14 2017 *)
%t A218348 Table[RootSum[1 + # - 2 #^2 - 2 #^3 - 3 #^4 + #^5 &, (-167 + 525 # - 73 #^2 + 819 #^3 - 218 #^4) #^n &]/2102, {n, 20}] (* _Eric W. Weisstein_, Jul 13 2017 *)
%o A218348 (PARI)
%o A218348 Vec((3+2*x+2*x^2-2*x^3-x^4)/(1-3*x-2*x^2-2*x^3+x^4+x^5)+O(x^50)) \\ _Andrew Howroyd_, May 10 2017
%Y A218348 Column 2 of A218354.
%Y A218348 Cf. A284663, A284702.
%K A218348 nonn,easy
%O A218348 1,1
%A A218348 _R. H. Hardin_, Oct 26 2012