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 A268769 Number of n X 3 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once. 1

%I #8 Jan 15 2019 07:54:09

%S 12,32,112,446,1524,5214,17000,54822,173244,541910,1676448,5146030,

%T 15683076,47518926,143238872,429867830,1285009740,3828046534,

%U 11368576272,33669165246,99465517716,293175780030,862355454792,2531766659654

%N Number of n X 3 0..2 arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.

%H R. H. Hardin, <a href="/A268769/b268769.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 2*a(n-2) - 16*a(n-3) - a(n-4) + 12*a(n-5) - 4*a(n-6) for n>8.

%F Empirical g.f.: 2*x*(6 - 8*x - 20*x^2 + 63*x^3 + 20*x^4 - 47*x^5 + 4*x^6 + 4*x^7) / (1 - 2*x - 3*x^2 + 2*x^3)^2. - _Colin Barker_, Jan 15 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 3 of A268774.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 13 2016

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Last modified June 4 23:50 EDT 2023. Contains 363130 sequences. (Running on oeis4.)