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R. H. Hardin, <a href="/A301843/b301843.txt">Table of n, a(n) for n = 1..210</a>
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Number of 3Xn 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.
4, 32, 139, 678, 3182, 15199, 72514, 346244, 1653214, 7893443, 37688062, 179946317, 859175558, 4102237937, 19586633161, 93518758201, 446516665710, 2131948036306, 10179244758257, 48602040050313, 232056341426270, 1107981178164225
1,1
Row 3 of A301841.
Empirical: a(n) = 4*a(n-1) +3*a(n-2) +3*a(n-3) +2*a(n-4) -2*a(n-5) +2*a(n-6) -7*a(n-7) -3*a(n-8) +5*a(n-9) -4*a(n-10) -3*a(n-11) +a(n-12) for n>14
Some solutions for n=5
..0..0..0..1..0. .0..1..0..1..1. .0..0..0..0..1. .0..1..0..0..1
..1..0..1..1..1. .1..1..0..0..1. .1..1..0..1..0. .1..1..0..0..1
..1..0..0..0..1. .0..1..1..0..1. .1..1..1..0..1. .0..1..0..0..0
Cf. A301841.
allocated
nonn
R. H. Hardin, Mar 27 2018
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