A183356 One quarter the number of n X 4 1..4 arrays with no two neighbors of any element equal to each other.
36, 576, 1296, 3600, 9216, 24336, 63504, 166464, 435600, 1140624, 2985984, 7817616, 20466576, 53582400, 140280336, 367258896, 961496064, 2517229584, 6590192400, 17253347904, 45169851024, 118256205456, 309598765056, 810540090000
Offset: 1
Keywords
Examples
Some solutions for 5 X 4 with a(1,1)=1: 1 4 3 3 1 1 4 4 1 2 4 1 1 4 2 2 1 1 3 4 2 4 1 1 4 2 3 1 3 2 4 1 1 4 3 3 2 2 3 1 3 3 2 2 4 2 3 1 4 1 3 3 3 2 1 1 3 4 4 2 1 1 4 4 3 1 4 4 4 1 2 2 3 2 4 4 3 1 1 3 4 2 3 1 3 1 2 2 2 3 4 1 1 1 3 2 4 2 2 4
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
Crossrefs
Cf. A183362.
Formula
Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3) for n>4.
Conjectures from Colin Barker, Mar 28 2018: (Start)
G.f.: 36*x*(1 + 14*x + 2*x^2 - 3*x^3) / ((1 + x)*(1 - 3*x + x^2)).
a(n) = (9/5)*2^(3-n)*((-1)^n*2^(2+n) + (3-sqrt(5))^(1+n) + (3+sqrt(5))^(1+n)) for n>1.
(End)
Assuming Colin Barker's conjectures, a(n) = (12*Fibonacci(n+1))^2, n>1. - Ehren Metcalfe, Apr 21 2018
Comments