|
%I #5 Mar 31 2012 12:36:29
%S 1,17,113,803,5855,41459,300943,2224023,16153497,116797601,851944533,
%T 6202923531,45107191789,328173759843,2387891294531,17373638032901,
%U 126409617048273,919727576644501,6691670125651177,48687601545703711
%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,3,1,1,1 for x=0,1,2,3,4
%C Every 0 is next to 0 4's, every 1 is next to 1 3's, every 2 is next to 2 1's, every 3 is next to 3 1's, every 4 is next to 4 1's
%C Column 4 of A197364
%H R. H. Hardin, <a href="/A197360/b197360.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) +25*a(n-2) +150*a(n-3) +414*a(n-4) -857*a(n-5) -9974*a(n-6) -42118*a(n-7) -67868*a(n-8) +291909*a(n-9) +1665950*a(n-10) +3428329*a(n-11) +810045*a(n-12) -23384598*a(n-13) -89246066*a(n-14) -146894491*a(n-15) +65409499*a(n-16) +914719497*a(n-17) +2219012323*a(n-18) +2086276830*a(n-19) -2516290285*a(n-20) -16891329383*a(n-21) -8932490107*a(n-22) +32645318584*a(n-23) -26461873134*a(n-24) -213227725865*a(n-25) -207243257310*a(n-26) -505793175949*a(n-27) +2898826155449*a(n-28) +7145836088511*a(n-29) -4629002872836*a(n-30) -2401405257780*a(n-31) -27307530798565*a(n-32) +59599301523601*a(n-33) -71872915971293*a(n-34) -134280224052192*a(n-35) +178887642807609*a(n-36) -470090079757467*a(n-37) +222856953175122*a(n-38) +1074246974800224*a(n-39) -596127798645363*a(n-40) +837976716887328*a(n-41) -652144155943248*a(n-42) -5992025098974012*a(n-43) +6264877490924760*a(n-44) +5326638416133696*a(n-45) -3126213675406656*a(n-46) -9240682701903840*a(n-47) +6180838932984192*a(n-48) +6548918601458304*a(n-49) -7829036052977664*a(n-50) +43487203235328*a(n-51) +1487460834902016*a(n-52) -303093721276416*a(n-53)
%e Some solutions containing all values 0 to 4 for n=5
%e ..0..0..0..0....1..3..1..0....1..0..2..1....0..0..0..0....2..1..0..0
%e ..1..3..1..2....1..1..0..0....3..1..1..3....0..1..3..1....1..3..0..1
%e ..0..1..4..1....3..1..2..0....1..4..1..1....1..4..1..2....2..1..1..3
%e ..2..1..1..3....1..4..1..0....2..1..3..1....3..1..1..0....0..1..4..1
%e ..1..3..1..1....2..1..3..1....0..0..0..0....1..1..3..1....1..3..1..2
%K nonn
%O 1,2
%A _R. H. Hardin_ Oct 14 2011
| 