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A198474 Number of 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to an odd number of horizontal and vertical neighbors. 2

%I #9 Mar 02 2018 06:27:16

%S 2,12,76,492,3212,21036,137932,904812,5936396,38950572,255572812,

%T 1676946156,11003350412,72199015212,473737530316,3108453529452,

%U 20396281280012,133831275048876,878140974959692,5761968373855212

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

%C Column 1 of A198477.

%H R. H. Hardin, <a href="/A198474/b198474.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 9*a(n-1) - 16*a(n-2).

%F Conjectures from _Colin Barker_, Mar 02 2018: (Start)

%F G.f.: 2*x*(1 - 3*x) / (1 - 9*x + 16*x^2).

%F a(n) = (2^(-4-n)*((9-sqrt(17))^n*(-5+3*sqrt(17)) + (9+sqrt(17))^n*(5+3*sqrt(17)))) / sqrt(17).

%F (End)

%e Some solutions for n=3:

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

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

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

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

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

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

%Y Cf. A198477.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 25 2011

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Last modified June 22 02:28 EDT 2024. Contains 373561 sequences. (Running on oeis4.)