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Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)
2

%I #5 Mar 31 2012 12:37:21

%S 122,2048,41932,931968,21472544,502504448,11838995200,279733684992,

%T 6617787903744,156641740131072,3708483510235904,87806041737925888,

%U 2079067090247547648,49228778299543155968,1165660962446546688768

%N Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors)

%C Column 7 of A208050

%H R. H. Hardin, <a href="/A208049/b208049.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 75*a(n-1) -2554*a(n-2) +55718*a(n-3) -900373*a(n-4) +11540175*a(n-5) -120646224*a(n-6) +1032906704*a(n-7) -7143273200*a(n-8) +38487096736*a(n-9) -148139743168*a(n-10) +301384072128*a(n-11) +434395534080*a(n-12) -4212812674816*a(n-13) -6055937053184*a(n-14) +188862038718976*a(n-15) -1113928611287040*a(n-16) +3311133232840704*a(n-17) -2101437137223680*a(n-18) -32416286559526912*a(n-19) +220131231030444032*a(n-20) -992034773109800960*a(n-21) +3717529494924165120*a(n-22) -11794027245416480768*a(n-23) +31236993687432921088*a(n-24) -70339147326082842624*a(n-25) +154801537571326263296*a(n-26) -448746548849001103360*a(n-27) +1717656393065237053440*a(n-28) -6299441128934805078016*a(n-29) +18664452298317869613056*a(n-30) -42448339422308433133568*a(n-31) +70184786763815892025344*a(n-32) -64759214749331813826560*a(n-33) -65052874836065503936512*a(n-34) +487617470914554383826944*a(n-35) -1485610864045675360813056*a(n-36) +3640029148467676101738496*a(n-37) -8283595658363681883815936*a(n-38) +17664539130299538596691968*a(n-39) -33111040019545470867079168*a(n-40) +49915764398968934926123008*a(n-41) -53360782694992243014500352*a(n-42) +27154724025092859785904128*a(n-43) +27407517485303035101970432*a(n-44) -87711501058877861501337600*a(n-45) +139238385451601130420174848*a(n-46) -222221580176017612232196096*a(n-47) +397056573879679769567559680*a(n-48) -556634782068810820628774912*a(n-49) +453347182355485940514816000*a(n-50) -154742504910672534362390528*a(n-51) for n>52

%e Some solutions for n=4

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Feb 22 2012