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A199704 T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum and no two neighbors equal.

%I A199704 #10 Jul 22 2025 13:23:04
%S A199704 1,1,2,1,4,6,1,6,14,8,1,8,32,52,14,1,10,52,168,200,32,1,12,82,380,892,
%T A199704 708,56,1,14,114,724,2734,4964,2642,100,1,16,156,1236,6504,20116,
%U A199704 27854,10000,204,1,18,200,1940,13324,59992,149942,156920,37984,388,1,20,254
%N A199704 T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum and no two neighbors equal.
%C A199704 Table starts
%C A199704 ...1......1.......1........1.........1..........1..........1...........1
%C A199704 ...2......4.......6........8........10.........12.........14..........16
%C A199704 ...6.....14......32.......52........82........114........156.........200
%C A199704 ...8.....52.....168......380.......724.......1236.......1940........2872
%C A199704 ..14....200.....892.....2734......6504......13324......24394.......41344
%C A199704 ..32....708....4964....20116.....59992.....147072.....314532......608420
%C A199704 ..56...2642...27854...149942....559028....1643204....4099204.....9059092
%C A199704 .100..10000..156920..1128388...5252900...18527516...53901956...136128432
%C A199704 .204..37984..891684..8545180..49700882..210316392..713719390..2059733054
%C A199704 .388.144876.5095360.65055556.472873888.2400684208.9503449352.31340655728
%H A199704 R. H. Hardin, <a href="/A199704/b199704.txt">Table of n, a(n) for n = 1..914</a>
%e A199704 Some solutions for n=6 k=5
%e A199704 ..0....5....1...-4...-2....1...-1...-5....4....0....3....0....2....2...-5...-1
%e A199704 ..5...-1....0....5...-5...-1...-2....4...-1....2...-1....4....3...-3....0....3
%e A199704 .-1...-3...-1....3....4....0...-5....2...-5...-1...-5....3...-4....4...-3....1
%e A199704 .-5...-5....3...-5...-4....1....0...-5....3....0....3...-1...-1...-3....5....4
%e A199704 ..4....4....0....0....2....2....3...-1....1....1....2...-2...-3...-5....0...-5
%e A199704 .-3....0...-3....1....5...-3....5....5...-2...-2...-2...-4....3....5....3...-2
%K A199704 nonn,tabl
%O A199704 1,3
%A A199704 _R. H. Hardin_ Nov 09 2011