A222835 Number of n X 5 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.

19, 384, 648, 1536, 4032, 9600, 22848, 55296, 133824, 322944, 779328, 1881600, 4542912, 10967424, 26477376, 63922176, 154322112, 372566400, 899454528, 2171475456, 5242405824, 12656287104, 30554979648, 73766246400, 178087472832

Offset

1,1

Comments

Column 5 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-3) + a(n-4) for n>7.

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

G.f.: x*(19 + 346*x - 120*x^2 + 202*x^3 + 173*x^4 - 144*x^5 - 72*x^6) / ((1 + x^2)*(1 - 2*x - x^2)).

a(n) = 48*((-1+i)*((-i)^n+i^(1+n)) + (1-sqrt(2))^n + (1+sqrt(2))^n) for n>3, where i=sqrt(-1).

(End)

Example

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

Crossrefs

Cf. A222838.

Sequence in context: A075839 A158592 A072359 * A094737 A009075 A221584

Adjacent sequences: A222832 A222833 A222834 * A222836 A222837 A222838

Keyword

nonn

Author

R. H. Hardin, Mar 06 2013

Status

approved