A198247 Number of 2n X 4 0..4 arrays with values 0..4 introduced in row major order and each element equal to exactly two horizontal and vertical neighbors.

1, 5, 40, 485, 6528, 90641, 1268648, 17794141, 249720000, 3505037833, 49198133832, 690571872597, 9693269289152, 136060470673025, 1909825721373608, 26807451423465421, 376285360845321600, 5281765543824353657

Offset

1,2

Comments

Column 2 of A198253.

Links

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

Formula

Empirical: a(n) = 20*a(n-1) -85*a(n-2) -16*a(n-3) +493*a(n-4) -124*a(n-5) -919*a(n-6) +120*a(n-7) +512*a(n-8).

Empirical g.f.: x*(1 - 15*x + 25*x^2 + 126*x^3 - 185*x^4 - 395*x^5 + 287*x^6 + 444*x^7) / ((1 - x)*(1 + x)*(1 - 4*x - x^2 + 8*x^3)*(1 - 16*x + 23*x^2 + 64*x^3)). - Colin Barker, May 14 2018

Example

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

Crossrefs

Cf. A198253.

Sequence in context: A201366 A281160 A282476 * A088695 A365779 A145166

Adjacent sequences: A198244 A198245 A198246 * A198248 A198249 A198250

Keyword

nonn

Author

R. H. Hardin Oct 22 2011

Status

approved