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

1,2

Comments

Column 2 of A185825.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Robert Israel, Maple-assisted proof of formula

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

Example

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

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

Prog

(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

Crossrefs

Cf. A185825.

Sequence in context: A056329 A190982 A082677 * A324354 A209667 A276754

Adjacent sequences: A185815 A185816 A185817 * A185819 A185820 A185821

Keyword

nonn

Author

R. H. Hardin, Feb 05 2011

Status

approved