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A208561 Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors. 1

%I #8 Jul 05 2018 07:21:53

%S 2,10,68,464,3168,21632,147712,1008640,6887424,47030272,321142784,

%T 2192900096,14974058496,102249267200,698201669632,4767619219456,

%U 32555340398592,222301769433088,1517971432275968,10365357302743040

%N Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.

%C Column 2 of A208567.

%H R. H. Hardin, <a href="/A208561/b208561.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 8*a(n-2) for n>3.

%F Conjectures from _Colin Barker_, Jul 05 2018: (Start)

%F G.f.: 2*x*(1 - x)*(1 - 2*x) / (1 - 8*x + 8*x^2).

%F a(n) = ((4-2*sqrt(2))^n*(-1+sqrt(2)) + (1+sqrt(2))*(2*(2+sqrt(2)))^n) / (8*sqrt(2)) for n>1.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A208567.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 28 2012

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)