A222834 Number of n X 4 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.

7, 96, 216, 600, 1536, 4056, 10584, 27744, 72600, 190104, 497664, 1302936, 3411096, 8930400, 23380056, 61209816, 160249344, 419538264, 1098365400, 2875557984, 7528308504, 19709367576, 51599794176, 135090015000, 353670250776

Offset

1,1

Comments

Column 4 of A222838.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3) for n>4.

Conjectures from Colin Barker, Aug 16 2018: (Start)

G.f.: x*(7 + 82*x + 10*x^2 - 17*x^3) / ((1 + x)*(1 - 3*x + x^2)).

a(n) = (3/5)*2^(2-n)*((-1)^n*2^(2+n) + (3-sqrt(5))^(1+n) + (3+sqrt(5))^(1+n)) for n>1.

(End)

Example

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

Crossrefs

Cf. A222838.

Sequence in context: A239999 A054932 A217240 * A327676 A338075 A177879

Adjacent sequences: A222831 A222832 A222833 * A222835 A222836 A222837

Keyword

nonn

Author

R. H. Hardin, Mar 06 2013

Status

approved