A198405 Number of 2n X 2 0..4 arrays with values 0..4 introduced in row major order and each element equal to exactly one horizontal and vertical neighbor.

2, 17, 377, 11473, 375273, 12456897, 414711897, 13814539697, 460231956937, 15333001667233, 510833776539193, 17018936996199057, 567002973887727017, 18890274083549781377, 629348476275500726297, 20967377362990867086193

Offset

1,1

Comments

Column 1 of A198408.

Links

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

Formula

Empirical: a(n) = 51*a(n-1) - 691*a(n-2) + 3601*a(n-3) - 7056*a(n-4) + 4096*a(n-5).

Conjectures from Colin Barker, Mar 02 2018: (Start)

G.f.: x*(2 - 85*x + 892*x^2 - 3209*x^3 + 3552*x^4) / ((1 - x)*(1 - 9*x + 16*x^2)*(1 - 41*x + 256*x^2)).

a(n) = (2^(-8-n)*(-1752*(9-sqrt(17))^n*(-51+5*sqrt(17)) + 1752*(9+sqrt(17))^n*(51+5*sqrt(17)) + 17*(73*2^(9+n) + (365-17*sqrt(73))*(41-3*sqrt(73))^n + (41+3*sqrt(73))^n*(365+17*sqrt(73))))) / 3723.

(End)

Example

Some solutions for n=3:
..0..0....0..0....0..1....0..0....0..0....0..0....0..0....0..1....0..0....0..1
..1..2....1..2....0..1....1..1....1..1....1..2....1..1....0..1....1..1....0..1
..1..2....1..2....2..3....2..3....2..3....1..2....2..2....2..2....0..0....2..3
..3..3....0..0....2..3....2..3....2..3....2..0....3..3....0..0....2..2....2..3
..4..0....3..2....1..0....3..0....4..4....2..0....4..4....1..3....0..0....4..4
..4..0....3..2....1..0....3..0....2..2....1..1....2..2....1..3....1..1....3..3

Crossrefs

Cf. A198408.

Sequence in context: A243509 A128159 A319591 * A202972 A085617 A152557

Adjacent sequences: A198402 A198403 A198404 * A198406 A198407 A198408

Keyword

nonn

Author

R. H. Hardin, Oct 24 2011

Status

approved