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A183356
One quarter the number of n X 4 1..4 arrays with no two neighbors of any element equal to each other.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 04 2011
STATUS
approved