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A208049 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).

%I A208049 #7 Jun 02 2025 07:42:58
%S A208049 122,2048,41932,931968,21472544,502504448,11838995200,279733684992,
%T A208049 6617787903744,156641740131072,3708483510235904,87806041737925888,
%U A208049 2079067090247547648,49228778299543155968,1165660962446546688768
%N A208049 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 A208049 Column 7 of A208050
%H A208049 R. H. Hardin, <a href="/A208049/b208049.txt">Table of n, a(n) for n = 1..210</a>
%F A208049 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 A208049 Some solutions for n=4
%e A208049 ..0..1..2..3..1..2..3....0..1..2..3..0..1..2....0..1..0..1..2..3..2
%e A208049 ..2..0..1..0..3..1..0....2..0..1..2..3..0..1....2..3..2..0..1..0..3
%e A208049 ..3..2..3..2..0..2..1....3..2..3..0..1..2..3....0..1..3..2..3..1..2
%e A208049 ..0..1..0..1..3..0..2....0..1..2..3..0..1..0....2..0..1..0..2..3..0
%K A208049 nonn
%O A208049 1,1
%A A208049 _R. H. Hardin_ Feb 22 2012