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%I #13 Oct 24 2024 03:13:53
%S 4,10,38,108,358,1132,3580,11382,36270,114992,365628,1162290,3692624,
%T 11733828,37293892,118504546,376583590,1196750110,3803034578,
%U 12085297922,38405269512,122045123484,387837623386,1232482503260,3916616317912
%N Number of nX5 0..4 arrays with each element equal to the number its horizontal and vertical zero neighbors.
%C Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 0's, every 3 is next to 3 0's, every 4 is next to 4 0's.
%C Column 5 of A197054.
%H R. H. Hardin, <a href="/A197051/b197051.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) +4*a(n-2) +10*a(n-3) +4*a(n-4) -20*a(n-5) +a(n-6) -2*a(n-7) +2*a(n-8) -16*a(n-9) +4*a(n-10) +a(n-13) for n>14.
%F Equivalent empirical g.f.: 4*x - 2*x^2*(5+14*x+15*x^2-x^3-39*x^4-8*x^5+6*x^6-21*x^7-13*x^8-x^9+x^10+3*x^11+3*x^12) / ( -1+x+4*x^2+10*x^3+4*x^4-20*x^5+x^6-2*x^7+2*x^8-16*x^9+4*x^10+x^13 ). - _R. J. Mathar_, Oct 10 2011
%e Some solutions for n=4
%e ..0..1..2..0..2....1..1..0..3..0....0..3..0..3..0....0..2..1..0..2
%e ..2..1..0..4..0....0..2..2..0..3....3..0..3..0..2....2..0..2..2..0
%e ..0..1..3..0..3....3..0..2..2..0....0..2..1..1..1....1..2..0..2..1
%e ..1..1..0..3..0....0..3..0..1..1....1..1..0..2..0....0..1..2..0..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 09 2011