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%I #5 Mar 31 2012 12:36:37
%S 1,1,2,1,4,6,1,4,12,8,1,6,24,24,14,1,8,42,72,82,32,1,8,60,152,256,232,
%T 56,1,10,84,256,804,1312,654,100,1,12,114,448,1836,5016,5206,2044,204,
%U 1,12,144,680,3196,12872,24864,21208,6096,388,1,14,180,952,6064,29864,77874
%N T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2)
%C Table starts
%C ...1.....1......1.......1........1.........1.........1..........1..........1
%C ...2.....4......4.......6........8.........8........10.........12.........12
%C ...6....12.....24......42.......60........84.......114........144........180
%C ...8....24.....72.....152......256.......448.......680........952.......1384
%C ..14....82....256.....804.....1836......3196......6064......10276......14846
%C ..32...232...1312....5016....12872.....29864.....62776.....114768.....200520
%C ..56...654...5206...24864....77874....216530....518560....1071202....2114394
%C .100..2044..21208..139148...547604...1699268...4854740...11588992...24551100
%C .204..6096..97668..814776..3784512..14546928..47329800..125461824..306360336
%C .388.18564.422052.4509164.25525476.116482068.436295060.1308549932.3582143596
%H R. H. Hardin, <a href="/A199909/b199909.txt">Table of n, a(n) for n = 1..871</a>
%F Empirical for rows:
%F T(1,k)=1
%F T(2,k)=a(k-1)+a(k-3)-a(k-4)
%F T(3,k)=2*a(k-1)-a(k-2)+a(k-3)-2*a(k-4)+a(k-5)
%F T(4,k)=a(k-1)+3*a(k-3)-3*a(k-4)-3*a(k-6)+3*a(k-7)+a(k-9)-a(k-10)
%F T(5,k)=a(k-1)+4*a(k-3)-4*a(k-4)-6*a(k-6)+6*a(k-7)+4*a(k-9)-4*a(k-10)-a(k-12)+a(k-13)
%F T(6,k)=2*a(k-1)-a(k-2)+4*a(k-3)-8*a(k-4)+4*a(k-5)-6*a(k-6)+12*a(k-7)-6*a(k-8)+4*a(k-9)-8*a(k-10)+4*a(k-11)-a(k-12)+2*a(k-13)-a(k-14)
%F T(7,k)=a(k-1)+6*a(k-3)-6*a(k-4)-15*a(k-6)+15*a(k-7)+20*a(k-9)-20*a(k-10)-15*a(k-12)+15*a(k-13)+6*a(k-15)-6*a(k-16)-a(k-18)+a(k-19)
%e Some solutions for n=7 k=6
%e .-6...-3....4...-6...-3....4....4...-6....4....3....0....3...-6...-6....0....4
%e .-4....2....2...-4...-4....3...-1...-1....5....2....4....4....4....5...-1...-6
%e ..4...-5....0...-3...-3....1....0....3...-5....4....0...-3...-6...-3...-5....4
%e .-4....6...-1....5....2...-6...-2....1...-4....0...-2...-1....1....1....0...-1
%e ..6....5....0....4....3....5...-6...-1...-6...-4...-4...-5...-1...-4...-2....0
%e .-2...-6....1....6....5...-3....2....6....2...-3....6....5....6....1....6...-4
%e ..6....1...-6...-2....0...-4....3...-2....4...-2...-4...-3....2....6....2....3
%Y Column 1 is A199697
%Y Row 2 is A063200(n+2)
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Nov 11 2011