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Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.
1

%I #8 Feb 22 2019 10:04:57

%S 4,36,234,1534,10291,68613,457178,3048314,20323497,135493938,

%T 903332290,6022478907,40151569213,267688593389,1784667144371,

%U 11898290761269,79325337411332,528858244821419,3525872716944031,23506825387232109

%N Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.

%H R. H. Hardin, <a href="/A295411/b295411.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) + 28*a(n-3) + 3*a(n-4) + 49*a(n-5) + 33*a(n-6) - 34*a(n-7) - 22*a(n-8).

%F Empirical g.f.: x*(4 + 12*x + 18*x^2 + 18*x^3 + 67*x^4 + 11*x^5 - 50*x^6 - 22*x^7) / (1 - 6*x - 28*x^3 - 3*x^4 - 49*x^5 - 33*x^6 + 34*x^7 + 22*x^8). - _Colin Barker_, Feb 22 2019

%e Some solutions for n=5:

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

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

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

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

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

%Y Column 3 of A295416.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 22 2017