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Number of n X 3 0..1 arrays with every element equal to 0, 1 or 3 horizontally or vertically adjacent elements, with upper left element zero.
1

%I #6 May 20 2021 12:37:59

%S 3,6,9,26,61,154,374,941,2357,5963,15074,38168,96641,244836,620311,

%T 1571854,3983147,10093850,25579490,64823479,164276135,416311227,

%U 1055023990,2673664936,6775663297,17171047596,43515284891,110277499816

%N Number of n X 3 0..1 arrays with every element equal to 0, 1 or 3 horizontally or vertically adjacent elements, with upper left element zero.

%C Column 3 of A301541.

%H R. H. Hardin, <a href="/A301536/b301536.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -a(n-2) -a(n-3) +2*a(n-4) -a(n-5) +3*a(n-6) -11*a(n-7) -a(n-8) +2*a(n-9) -4*a(n-10) -2*a(n-11) -a(n-12) +11*a(n-13) +3*a(n-14) +a(n-15) +2*a(n-16) +a(n-17) -a(n-18) -3*a(n-19) -a(n-20).

%e Some solutions for n=5

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

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

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

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

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

%Y Cf. A301541.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 23 2018