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 A202006 T(n,k)=Number of -k..k circular arrays x(0..n+1) of n+2 elements with zero sums of x(i) and x(i)*x((i+1) mod (n+2)) 13

%I #5 Mar 31 2012 12:36:46

%S 1,1,9,1,25,11,1,49,31,43,1,81,61,247,85,1,121,101,601,799,329,1,169,

%T 111,1357,2605,4281,577,1,225,231,2467,7463,22865,15751,1921,1,289,

%U 261,4327,14365,80065,101395,61581,4115,1,361,361,6385,33699,221433,490879,657871

%N T(n,k)=Number of -k..k circular arrays x(0..n+1) of n+2 elements with zero sums of x(i) and x(i)*x((i+1) mod (n+2))

%C Table starts

%C .....1.......1........1.........1..........1..........1...........1...........1

%C .....9......25.......49........81........121........169.........225.........289

%C ....11......31.......61.......101........111........231.........261.........361

%C ....43.....247......601......1357.......2467.......4327........6385........9445

%C ....85.....799.....2605......7463......14365......33699.......53775.......90007

%C ...329....4281....22865.....80065.....221433.....511257.....1039409.....1942577

%C ...577...15751...101395....490879....1519417....4460689.....9882793....21851983

%C ..1921...61581...657871...3697331...14540551...48525711...128920651...308155711

%C ..4115..267037..3603821..28156261..130169953..529141383..1579308193..4407995417

%C .14331.1298599.25726609.240962805.1459090675.6524977447.23513859009.72520540045

%H R. H. Hardin, <a href="/A202006/b202006.txt">Table of n, a(n) for n = 1..311</a>

%e Some solutions for n=5 k=3

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

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

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

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

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

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

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

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_ Dec 07 2011

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