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

1,1

Comments

Column 4 of A183362.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

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

Example

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

Crossrefs

Cf. A183362.

Sequence in context: A159656 A081447 A218311 * A099764 A003841 A226284

Adjacent sequences: A183353 A183354 A183355 * A183357 A183358 A183359

Keyword

nonn

Author

R. H. Hardin, Jan 04 2011

Status

approved