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A222139 Number of n X 3 0..4 arrays with no entry increasing mod 5 by 4 rightwards or downwards, starting with upper left zero. 2

%I

%S 16,676,28564,1206964,50999956,2154990196,91058563924,3847656513844,

%T 162581749707796,6869850581244916,290283793189916884,

%U 12265868026121849524,518291141165452870036,21900260661415244606836

%N Number of n X 3 0..4 arrays with no entry increasing mod 5 by 4 rightwards or downwards, starting with upper left zero.

%C Column 3 of A222144.

%H R. H. Hardin, <a href="/A222139/b222139.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 45*a(n-1) - 116*a(n-2).

%F Conjectures from _Colin Barker_, Mar 14 2018: (Start)

%F G.f.: 4*x*(4 - 11*x) / (1 - 45*x + 116*x^2).

%F a(n) = (2^(-1-n)*((45-sqrt(1561))^n*(-433+11*sqrt(1561)) + (45+sqrt(1561))^n*(433+11*sqrt(1561)))) / (29*sqrt(1561)).

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A222144.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 09 2013

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Last modified October 4 21:22 EDT 2022. Contains 357240 sequences. (Running on oeis4.)