A218836 Unmatched value maps: number of n X 2 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 2 array.

1, 2, 7, 21, 65, 200, 616, 1897, 5842, 17991, 55405, 170625, 525456, 1618192, 4983377, 15346786, 47261895, 145547525, 448227521, 1380359512, 4250949112, 13091204281, 40315615410, 124155792775, 382349636061, 1177482265857, 3626169232672, 11167134898976

Offset: 0

Author

R. H. Hardin, Nov 07 2012

Keywords

• nonn
• easy

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 0..210
• Index entries for linear recurrences with constant coefficients, signature (2,3,1).

Crossrefs

Column 2 of A218842.

Programs

Maple

a:= n-> (<<0|1|0>, <0|0|1>, <1|3|2>>^n. <<1, 2, 7>>)[1$2]:
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 21 2020

Mathematica

LinearRecurrence[{2, 3, 1}, {1, 2, 7}, 30] (* Paolo Xausa, Jan 29 2025 *)

Formula

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

G.f.: Q(0)/2 , where Q(k) = 1 + 1/(1- x*(4*k+2 +3*x+x^2)/(x*(4*k+4 +3*x+x^2) + 1/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Oct 04 2013

G.f.: 1/(1-2*x-3*x^2-x^3). - Alois P. Heinz, Apr 21 2020

Extensions

a(0)=1 prepended and first g.f. adapted by Alois P. Heinz, Apr 21 2020