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A195973 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,3,4 for x=0,1,2,3,4. 1

%I #9 May 08 2018 06:19:54

%S 4,14,24,36,67,134,240,432,803,1501,2764,5118,9519,17718,32927,61310,

%T 114257,213023,397223,741197,1383497,2583168,4824204,9012010,16838364,

%U 31466993,58813148,109939804,205534006,384287357,718564103,1343717638

%N Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,3,4 for x=0,1,2,3,4.

%C Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's.

%C Column 3 of A195978.

%H R. H. Hardin, <a href="/A195973/b195973.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-1) +a(n-3) +a(n-4) -6*a(n-5) -a(n-6) -4*a(n-7) +2*a(n-8) +2*a(n-9) +5*a(n-10) +2*a(n-11) -2*a(n-14) -a(n-15).

%F Empirical g.f.: x*(4 + 6*x - 4*x^2 - 16*x^3 - 23*x^4 - 14*x^5 + 23*x^7 + 26*x^8 + 19*x^9 + 9*x^10 - x^11 - 7*x^12 - 5*x^13 - x^14) / ((1 - x)*(1 + x^2)*(1 - x - x^2)*(1 - x^2 - 2*x^3 - 4*x^4 - 2*x^5 - x^6 + x^7 + x^8 + 2*x^9 + x^10)). - _Colin Barker_, May 08 2018

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A195978.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 25 2011

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Last modified July 20 23:17 EDT 2024. Contains 374461 sequences. (Running on oeis4.)