A198535 Number of 2n X 2 0..4 arrays with values 0..4 introduced in row major order and each element equal to an even number of horizontal and vertical neighbors.

5, 404, 67442, 11739910, 2048681430, 357559607382, 62405998006614, 10891920070833494, 1901001993638057302, 331788019307198829910, 57908034887329483937110, 10106876407223511717074262

Offset

1,1

Comments

Column 1 of A198538.

Links

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

Formula

Empirical: a(n) = 189*a(n-1) -2572*a(n-2) +8272*a(n-3) -9984*a(n-4) +4096*a(n-5) for n>6.

Empirical g.f.: x*(5 - 541*x + 3946*x^2 - 8900*x^3 + 7296*x^4 - 1536*x^5) / ((1 - x)*(1 - 12*x + 16*x^2)*(1 - 176*x + 256*x^2)). - Colin Barker, May 14 2018

Example

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

Crossrefs

Cf. A198538.

Sequence in context: A195502 A189307 A198538 * A128866 A221047 A368021

Adjacent sequences: A198532 A198533 A198534 * A198536 A198537 A198538

Keyword

nonn

Author

R. H. Hardin, Oct 26 2011

Status

approved