A197371 - OEIS

%I #5 Mar 31 2012 12:36:29

%S 1,41,646,4023,50831,509018,5198997,54278107,559939403,5785336959,

%T 59865826196,618821603760,6398319110978,66160018680427,

%U 684049467447585,7072850485476387,73130794356723859,756143068281744553

%N Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,4,1,0,1 for x=0,1,2,3,4

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

%C Column 6 of A197373

%H R. H. Hardin, <a href="/A197371/b197371.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) +43*a(n-2) +215*a(n-3) +250*a(n-4) +173*a(n-5) -4379*a(n-6) -34939*a(n-7) -90229*a(n-8) +111072*a(n-9) +429595*a(n-10) +1158260*a(n-11) +4642261*a(n-12) -12087753*a(n-13) -5962742*a(n-14) -16663480*a(n-15) -36444768*a(n-16) +156871067*a(n-17) +115506448*a(n-18) +746746879*a(n-19) -476961404*a(n-20) -1663273438*a(n-21) -8866676697*a(n-22) +2263864401*a(n-23) -10070372221*a(n-24) +42622852325*a(n-25) +56430984216*a(n-26) +26335493106*a(n-27) +160126357302*a(n-28) -520561946179*a(n-29) -44086950153*a(n-30) -778868877415*a(n-31) -61704718747*a(n-32) +1314860786512*a(n-33) -34444392258*a(n-34) +4391629730413*a(n-35) -28588255225*a(n-36) +1248977828921*a(n-37) -2752263434107*a(n-38) -558388249884*a(n-39) -5381872685129*a(n-40) -4806100476029*a(n-41) -16157659096139*a(n-42) +13187720707324*a(n-43) -21990551271236*a(n-44) +6556389839941*a(n-45) +28293929786717*a(n-46) -39028737321736*a(n-47) +55862192759828*a(n-48) -24884405362826*a(n-49) +1671411262353*a(n-50) +36465501447605*a(n-51) -28226800017962*a(n-52) +22616686907989*a(n-53) +2934917133570*a(n-54) -17288535294392*a(n-55) +3457524724654*a(n-56) +717315220618*a(n-57) -4478038144504*a(n-58) -326968281449*a(n-59) +112857059601*a(n-60) -1181145682958*a(n-61) +873137467112*a(n-62) +1113768481537*a(n-63) +122401417651*a(n-64) -237470675662*a(n-65) -136972192909*a(n-66) -15120034789*a(n-67) +27108126663*a(n-68) +14177204309*a(n-69) -2997879816*a(n-70) -3454409092*a(n-71) -675367204*a(n-72) +229768552*a(n-73) +186458496*a(n-74) +40577520*a(n-75) -148976*a(n-76) -2121152*a(n-77) -188736*a(n-78) -9984*a(n-79) +1280*a(n-80)

%e Some solutions containing all values 0 to 4 for n=4

%e ..0..0..0..3..0..0....0..0..3..0..0..0....0..0..3..0..1..2....0..1..2..2..1..2

%e ..0..1..0..0..1..0....0..3..0..0..1..0....0..0..0..1..4..1....1..4..1..1..4..1

%e ..1..4..1..1..4..1....0..3..0..1..4..1....3..0..0..0..1..0....0..1..0..0..1..0

%e ..2..1..2..2..1..0....0..0..3..0..1..2....0..0..3..0..0..0....0..0..0..3..0..0

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 14 2011