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A269761 Number of n X 2 0..5 arrays with some element plus some horizontally or vertically adjacent neighbor totalling five exactly once. 1

%I

%S 6,480,17520,524160,14288400,368958240,9195061680,223482006720,

%T 5331222081360,125355762453600,2913873085171440,67100778335162880,

%U 1533214659516235920,34803572453875078560,785602378216093258800

%N Number of n X 2 0..5 arrays with some element plus some horizontally or vertically adjacent neighbor totalling five exactly once.

%H R. H. Hardin, <a href="/A269761/b269761.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 42*a(n-1) - 441*a(n-2) for n>3.

%F Conjectures from _Colin Barker_, Jan 28 2019: (Start)

%F G.f.: 6*x*(1 + 38*x + x^2) / (1 - 21*x)^2.

%F a(n) = 80 * 3^(n-2) * 7^(n-3) * (31*n-20) for n>1.

%F (End)

%e Some solutions for n=3:

%e ..5..3. .4..0. .0..4. .0..4. .2..3. .5..4. .0..3. .2..5. .4..4. .4..4

%e ..1..4. .1..0. .0..3. .0..5. .5..5. .2..1. .1..4. .4..2. .2..5. .1..2

%e ..3..0. .0..4. .5..3. .4..5. .1..5. .0..0. .5..5. .4..1. .0..0. .2..4

%Y Column 2 of A269767.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 04 2016

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Last modified January 15 08:51 EST 2021. Contains 340186 sequences. (Running on oeis4.)