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A299591 Number of n X 4 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 1

%I

%S 5,5,11,23,53,121,250,533,1162,2490,5327,11465,24641,52882,113593,

%T 244046,524134,1125735,2418077,5193785,11155562,23961133,51466258,

%U 110544050,237437407,509992017,1095411137,2352832034,5053646321,10854722326

%N Number of n X 4 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Column 4 of A299595.

%H R. H. Hardin, <a href="/A299591/b299591.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9.

%F Empirical g.f.: x*(5 + x^2 - 8*x^3 - x^4 + 12*x^5 + 6*x^6 - 4*x^7 - 3*x^8) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - _Colin Barker_, Feb 15 2018

%e Some solutions for n=5:

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

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

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

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

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

%Y Cf. A299595.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 13 2018

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Last modified August 13 05:18 EDT 2022. Contains 356077 sequences. (Running on oeis4.)