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 A198535 Number of 2n X 2 0..4 arrays with values 0..4 introduced in row major order and each element equal to an even number of horizontal and vertical neighbors. 1

%I #10 May 14 2018 14:23:21

%S 5,404,67442,11739910,2048681430,357559607382,62405998006614,

%T 10891920070833494,1901001993638057302,331788019307198829910,

%U 57908034887329483937110,10106876407223511717074262

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

%C Column 1 of A198538.

%H R. H. Hardin, <a href="/A198535/b198535.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 189*a(n-1) -2572*a(n-2) +8272*a(n-3) -9984*a(n-4) +4096*a(n-5) for n>6.

%F Empirical g.f.: x*(5 - 541*x + 3946*x^2 - 8900*x^3 + 7296*x^4 - 1536*x^5) / ((1 - x)*(1 - 12*x + 16*x^2)*(1 - 176*x + 256*x^2)). - _Colin Barker_, May 14 2018

%e Some solutions for n=3:

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

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

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

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

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

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

%Y Cf. A198538.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 26 2011

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Last modified September 11 13:40 EDT 2024. Contains 375836 sequences. (Running on oeis4.)