login
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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 06 2013
STATUS
approved