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 A186161 1/4 the number of n X 2 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors. 1

%I #8 Apr 17 2018 11:24:22

%S 1,7,48,321,2175,14748,99933,677283,4590168,31108893,210834267,

%T 1428886932,9683993481,65631317487,444803049600,3014563174089,

%U 20430595384935,138464249604684,938413592805957,6359909317239723

%N 1/4 the number of n X 2 0..3 arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.

%C Column 2 of A186168.

%H R. H. Hardin, <a href="/A186161/b186161.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 5*a(n-1) + 11*a(n-2) + 9*a(n-3) - 9*a(n-4) - 27*a(n-5).

%F Empirical g.f.: x*(1 + 2*x + 2*x^2 - 5*x^3 - 12*x^4) / (1 - 5*x - 11*x^2 - 9*x^3 + 9*x^4 + 27*x^5). - _Colin Barker_, Apr 17 2018

%e Some solutions for 4 X 2 with a(1,1)=0:

%e ..0..0....0..1....0..0....0..0....0..3....0..2....0..0....0..2....0..2....0..0

%e ..2..2....0..1....2..3....1..1....0..3....0..2....0..2....0..2....0..2....0..0

%e ..0..2....3..3....2..3....3..3....2..0....0..2....3..2....3..3....1..1....2..2

%e ..0..0....0..0....1..1....3..3....2..0....0..2....3..3....3..3....1..1....0..0

%Y Cf. A186168.

%K nonn

%O 1,2

%A _R. H. Hardin_, Feb 13 2011

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Last modified June 8 14:02 EDT 2023. Contains 363165 sequences. (Running on oeis4.)