A202900 Number of n X 2 0..1 arrays with every one equal to some NW, E or S neighbor.

1, 1, 4, 14, 40, 116, 344, 1016, 2992, 8816, 25984, 76576, 225664, 665024, 1959808, 5775488, 17020160, 50157824, 147813376, 435600896, 1283700736, 3783021568, 11148433408, 32854046720, 96819736576, 285324406784, 840841134080, 2477929668608, 7302372818944, 21519839510528

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000 (terms n = 1..210 from R. H. Hardin)

Index entries for linear recurrences with constant coefficients, signature (4,-4,4,-4).

Formula

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

G.f.: -(x-1)*(2*x^2-2*x+1) / (1 - 4*x + 4*x^2 - 4*x^3 + 4*x^4). - Colin Barker, Jun 02 2018

Example

Some solutions for n=5:
..1..1....0..0....1..1....1..0....0..1....1..0....1..0....1..1....1..0....1..1
..0..1....0..0....1..1....1..0....0..1....1..1....1..0....0..1....1..1....1..1
..0..0....1..0....0..0....1..1....0..1....1..1....1..0....1..1....0..0....0..1
..1..1....1..1....1..0....0..1....1..1....0..1....1..0....1..1....1..1....1..1
..1..1....0..1....1..1....0..0....1..1....0..0....1..1....0..1....1..1....1..1

Crossrefs

Column 2 of A202906.

Sequence in context: A054443 A281766 A072674 * A238117 A032285 A196451

Adjacent sequences: A202897 A202898 A202899 * A202901 A202902 A202903

Keyword

nonn,easy

Author

R. H. Hardin, Dec 25 2011

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 14 2026

Status

approved