A196742 - OEIS

%I #10 Oct 06 2019 18:23:08

%S 1,7,71,401,2923,19567,134507,919377,6283897,42987489,293903925,

%T 2009922151,13744157339,93985887721,642701573055,4394944856905,

%U 30053778082923,205515234410701,1405365233289259,9610242269541951

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

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

%C Column 4 of A196746.

%H R. H. Hardin, <a href="/A196742/b196742.txt">Table of n, a(n) for n = 1..200</a>

%H Robert Israel, <a href="/A196742/a196742.pdf">Maple-assisted proof of empirical formula</a>

%F Empirical: a(n) = 3*a(n-1) + 26*a(n-2) + 16*a(n-3) - 99*a(n-4) + 2*a(n-5) + 81*a(n-6) - 330*a(n-7) + 340*a(n-8) - 212*a(n-9) + 124*a(n-10) + 81*a(n-11) - 30*a(n-12) + 5*a(n-13) - 3*a(n-14) - a(n-15).

%F Empirical formula verified: see link. - _Robert Israel_, Oct 06 2019

%e Some solutions for n=5:

%e   0 0 3 0     0 0 0 0     0 3 0 0     0 0 3 0     0 0 0 0

%e   3 0 0 3     0 0 0 3     0 0 0 0     0 0 0 3     0 3 3 0

%e   0 3 1 0     3 0 1 0     0 3 0 3     0 3 1 0     0 0 0 3

%e   0 0 0 3     0 0 3 0     0 3 0 0     3 0 0 3     1 3 0 0

%e   0 3 0 0     0 3 0 0     0 0 0 0     0 0 3 0     0 0 0 0

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 06 2011