A185818 1/5 the number of n X 2 0..4 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

1, 9, 76, 656, 5680, 49248, 426928, 3701360, 32089696, 278208816, 2411993584, 20911320416, 181295389360, 1571781109104, 13626909445216, 118141552910384, 1024254735084784, 8880006538838880, 76987211704914352, 667457928119357552

Offset: 1

Author

R. H. Hardin, Feb 05 2011

Keywords

• nonn

Comments

Column 2 of A185825.

Examples

			Some solutions for 4 X 2 with a(1,1)=0:
..0..2....0..0....0..0....0..0....0..0....0..0....0..3....0..0....0..0....0..0
..0..2....1..1....0..0....0..3....3..2....2..0....0..3....3..4....0..2....0..3
..1..1....1..1....4..4....4..3....3..2....2..0....2..3....3..4....4..2....3..3
..0..0....0..0....3..3....4..3....3..3....1..1....2..2....3..4....4..2....2..2
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200
• Robert Israel, Maple-assisted proof of formula

Crossrefs

Cf. A185825.

Programs

Maple

f:= gfun:-rectoproc({a(n) = 7*a(n-1) + 15*a(n-2) - 32*a(n-4) - 64*a(n-5), a(1)=1, a(2)=9, a(3)=76, a(4)=656, a(5)=5680},a(n),remember):
map(f, [$1..30]); # Robert Israel, Jul 23 2018

PARI

x='x+O('x^99); Vec(x*(1+2*x-2*x^2-11*x^3-20*x^4)/(1-7*x-15*x^2+32*x^4+64*x^5)) \\ Altug Alkan, Jul 23 2018

Formula

Empirical: a(n) = 7*a(n-1) + 15*a(n-2) - 32*a(n-4) - 64*a(n-5).

Empirical g.f.: x*(1 + 2*x - 2*x^2 - 11*x^3 - 20*x^4) / (1 - 7*x - 15*x^2 + 32*x^4 + 64*x^5). - Colin Barker, Apr 16 2018

Empirical formulas verified (see link). - Robert Israel, Jul 23 2018