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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A222838.
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)
Comments