A197075 - OEIS

%I #8 May 24 2021 14:39:02

%S 4,34,205,1407,9492,65251,445506,3041309,20782756,142011656,970224226,

%T 6628930320,45292120759,309453920284,2114314490865,14445886493697,

%U 98700314097726,674361537935123,4607518893055747,31480487717138869

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

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

%C Column 4 of A197079.

%H R. H. Hardin, <a href="/A197075/b197075.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +8*a(n-2) +54*a(n-3) -75*a(n-4) -434*a(n-5) -752*a(n-6) -1078*a(n-7) +791*a(n-8) -3146*a(n-9) -15224*a(n-10) +19955*a(n-11) +100377*a(n-12) +81917*a(n-13) -151559*a(n-14) -390580*a(n-15) +16406*a(n-16) +611894*a(n-17) +124237*a(n-18) -818739*a(n-19) -420962*a(n-20) +1082532*a(n-21) +951355*a(n-22) -892542*a(n-23) -923270*a(n-24) +455635*a(n-25) +964289*a(n-26) +28594*a(n-27) -1633341*a(n-28) -414999*a(n-29) +1608705*a(n-30) +118045*a(n-31) -615922*a(n-32) -298043*a(n-33) -323708*a(n-34) +1264162*a(n-35) +222043*a(n-36) -1144097*a(n-37) +204507*a(n-38) +366722*a(n-39) -85620*a(n-40) -160944*a(n-41) +48884*a(n-42) +18196*a(n-43) +21482*a(n-44) -17444*a(n-45) -9480*a(n-46) +17687*a(n-47) -3490*a(n-48) -4493*a(n-49) +448*a(n-50) +1855*a(n-51) -1096*a(n-52) +211*a(n-53) +94*a(n-54) -62*a(n-55) +13*a(n-56) -3*a(n-57) +a(n-58).

%e Some solutions for n=5

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

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

%e ..0..0..1..0....0..4..0..0....0..1..1..0....0..4..0..0....1..2..2..0

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

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

%Y Cf. A197079.

%K nonn

%O 1,1

%A _R. H. Hardin_ Oct 09 2011