login
Number of nX4 0..4 arrays with each element equal to the number its horizontal and vertical neighbors equal to itself
1

%I #5 Mar 31 2012 12:36:25

%S 1,1,7,21,48,118,222,527,1370,3336,7717,17897,41296,98631,236602,

%T 554717,1304489,3078621,7242849,17138388,40496052,95320672,224944921,

%U 530817100,1251705990,2954749967,6970501275,16438448824,38788768683,91508873268

%N Number of nX4 0..4 arrays with each element equal to the number its horizontal and vertical neighbors equal to itself

%C Column 4 of A195969

%H R. H. Hardin, <a href="/A195965/b195965.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 6*a(n-3) +2*a(n-4) +19*a(n-5) +32*a(n-6) +22*a(n-7) +2*a(n-8) -31*a(n-9) +42*a(n-10) -133*a(n-11) -145*a(n-12) -88*a(n-13) -150*a(n-14) +149*a(n-15) -444*a(n-16) +236*a(n-17) +468*a(n-18) +54*a(n-19) +350*a(n-20) +126*a(n-21) +804*a(n-22) -1320*a(n-24) +640*a(n-25) +384*a(n-26) -704*a(n-27) for n>29

%e Some solutions for n=5

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

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

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

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

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

%K nonn

%O 1,3

%A _R. H. Hardin_ Sep 25 2011