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A198247 Number of 2n X 4 0..4 arrays with values 0..4 introduced in row major order and each element equal to exactly two horizontal and vertical neighbors. 1

%I

%S 1,5,40,485,6528,90641,1268648,17794141,249720000,3505037833,

%T 49198133832,690571872597,9693269289152,136060470673025,

%U 1909825721373608,26807451423465421,376285360845321600,5281765543824353657

%N Number of 2n X 4 0..4 arrays with values 0..4 introduced in row major order and each element equal to exactly two horizontal and vertical neighbors.

%C Column 2 of A198253.

%H R. H. Hardin, <a href="/A198247/b198247.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 20*a(n-1) -85*a(n-2) -16*a(n-3) +493*a(n-4) -124*a(n-5) -919*a(n-6) +120*a(n-7) +512*a(n-8).

%F Empirical g.f.: x*(1 - 15*x + 25*x^2 + 126*x^3 - 185*x^4 - 395*x^5 + 287*x^6 + 444*x^7) / ((1 - x)*(1 + x)*(1 - 4*x - x^2 + 8*x^3)*(1 - 16*x + 23*x^2 + 64*x^3)). - _Colin Barker_, May 14 2018

%e Some solutions for n=3:

%e ..0..0..0..0....0..0..1..1....0..0..1..1....0..0..0..0....0..0..1..1

%e ..0..1..1..0....0..0..1..1....0..0..1..1....0..1..1..0....0..0..1..1

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

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

%e ..2..2..3..3....0..0..1..1....0..0..4..4....1..1..2..2....0..0..3..3

%e ..2..2..3..3....0..0..1..1....0..0..4..4....1..1..2..2....0..0..3..3

%Y Cf. A198253.

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 22 2011

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Last modified January 30 19:55 EST 2023. Contains 359947 sequences. (Running on oeis4.)