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.

3, 11, 41, 149, 547, 2007, 7361, 27001, 99043, 363299, 1332617, 4888173, 17930307, 65770159, 241251521, 884934705, 3246028995, 11906758971, 43675182633, 160204937605, 587647732323, 2155550649479, 7906775346689, 29002842683433

Offset: 1

Author

R. H. Hardin, Oct 26 2012

Keywords

• nonn
• easy

Comments

Number of dominating sets in the ladder graph P_2 X P_n. - Andrew Howroyd, May 10 2017

Examples

			Some solutions for n=3
..1..0....1..1....0..1....1..0....1..1....1..1....0..1....0..0....1..0....0..1
..1..0....0..0....1..1....1..0....0..1....1..1....0..1....1..1....0..0....0..0
..0..1....1..1....0..1....1..0....1..0....1..0....1..0....0..0....0..1....1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Eric Weisstein's World of Mathematics, Dominating Set
• Eric Weisstein's World of Mathematics, Ladder Graph
• Index entries for linear recurrences with constant coefficients, signature (3,2,2,-1,-1).

Crossrefs

Column 2 of A218354.

Cf. A284663, A284702.

Programs

Mathematica

LinearRecurrence[{3, 2, 2, -1, -1}, {3, 11, 41, 149, 547}, 20]  (* Eric W. Weisstein, Jun 14 2017 *)
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 *)
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 *)

PARI

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

Formula

a(n) = 3*a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) -a(n-5).

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