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%I #4 Apr 13 2012 14:36:01
%S 39,221,1205,6467,34121,177699,915213,4669391,23634429,118812727,
%T 593811441,2952974203,14621731205,72132302495,354709008197,
%U 1739483827823,8510158543657,41549694953587,202504122129701,985469127469735
%N Number of -3..3 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having one, three or four distinct values for every i<=n and j<=n
%H R. H. Hardin, <a href="/A211503/b211503.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 25*a(n-1) -86*a(n-2) -2766*a(n-3) +23247*a(n-4) +119511*a(n-5) -1816907*a(n-6) -1574319*a(n-7) +82177349*a(n-8) -80086855*a(n-9) -2544562219*a(n-10) +5233419501*a(n-11) +58355698297*a(n-12) -162820706903*a(n-13) -1038587068889*a(n-14) +3432535121071*a(n-15) +14802727614020*a(n-16) -53791218025674*a(n-17) -172734790259807*a(n-18) +651236422650137*a(n-19) +1673935940750700*a(n-20) -6198185244826844*a(n-21) -13547457654687744*a(n-22) +46657431196628188*a(n-23) +91183889759752412*a(n-24) -277464963716582740*a(n-25) -503244480078414108*a(n-26) +1296483650559001036*a(n-27) +2226208616402273320*a(n-28) -4731973333934855704*a(n-29) -7668189725072349984*a(n-30) +13488906625705777888*a(n-31) +19913542838860968768*a(n-32) -30400496999649986752*a(n-33) -37743504017134533824*a(n-34) +55219282681252131136*a(n-35) +50312571418640076416*a(n-36) -80714620361403032192*a(n-37) -43048893834396547072*a(n-38) +91858751622728153600*a(n-39) +15377448229443087360*a(n-40) -76554717071384068096*a(n-41) +12569054979688185856*a(n-42) +42186501659922612224*a(n-43) -20980813531597193216*a(n-44) -11942638263898144768*a(n-45) +12698021906726846464*a(n-46) -618436227085631488*a(n-47) -3502870289992646656*a(n-48) +1472014657436254208*a(n-49) +192136320744685568*a(n-50) -334040726799122432*a(n-51) +94469527294705664*a(n-52) +6296177226022912*a(n-53) -11509731541647360*a(n-54) +3579027117834240*a(n-55) -576235361009664*a(n-56) +49941879717888*a(n-57) -1855425871872*a(n-58)
%e Some solutions for n=5
%e ..3....1...-2...-1...-2....3....3....3...-2....2...-1....0...-1...-2....1....0
%e .-2....3....3...-3....0...-3....2....1....1...-1...-3...-3...-2....0....3...-2
%e ..3....1....2...-1...-2....3....3....0....3...-3....3....2....0....2...-2...-1
%e ..2....3...-2....2....1...-2....2....0....0....3....0....3....0....0...-1....0
%e ..0....0....3....3....0....0....1...-3....3...-2...-3....0....0....0...-3....2
%e ..3...-3....0....2....2...-3....3....0...-2....2....0....0...-1...-2...-1....0
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 13 2012
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