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

1,1

Comments

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

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).

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

Example

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

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 *)

Prog

(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

Crossrefs

Column 2 of A218354.

Cf. A284663, A284702.

Sequence in context: A242233 A294504 A086972 * A320827 A335793 A077831

Adjacent sequences: A218345 A218346 A218347 * A218349 A218350 A218351

Keyword

nonn,easy

Author

R. H. Hardin, Oct 26 2012

Status

approved