%I #7 Aug 19 2022 12:37:36
%S 1,1,3,1,9,11,1,11,31,21,1,19,65,107,61,1,25,109,243,501,179,1,31,143,
%T 541,1731,2339,447,1,33,207,839,4769,11251,10303,1243,1,41,245,1531,
%U 10135,40483,67083,44523,3359,1,43,337,2145,21411,106047,327223,426379
%N T(n,k) = Number of strings of n+2 numbers x(i) in -k..k with the sum of x(i) equal to zero and the sums of x(i)*x(i+1) and x(i)*x(i+2) equal to each other.
%C Table starts
%C ....1......1........1........1.......1.......1......1......1.....1....1...1..1
%C ....3......9.......11.......19......25......31.....33.....41....43...53..59.75
%C ...11.....31.......65......109.....143.....207....245....337...427..491.573
%C ...21....107......243......541.....839....1531...2145...3345..4477.6181
%C ...61....501.....1731.....4769...10135...21411..35451..59353.89619
%C ..179...2339....11251....40483..106047..251231.496519.945243
%C ..447..10303....67083...327223.1015445.2880959
%C .1243..44523...426379..2590527.9974135
%C .3359.198695..2719451.20896283
%C .9465.888601.17387313
%H R. H. Hardin, <a href="/A184061/b184061.txt">Table of n, a(n) for n = 1..84</a>
%e Some solutions for n=5, k=4
%e ..3....3....1....1...-1....2....3....0....1....1...-2...-1...-1...-2....1....2
%e ..1...-2....0...-4...-2....1....0...-1...-4....0...-2....0...-2...-2...-2....3
%e .-4...-4...-4....0...-4...-2...-2....2...-1....2...-3....2....0...-1...-1...-1
%e ..2....2....1...-2....4...-4....1....4....1....0....2....1....0....0....1....4
%e .-1....1....0....0....1....2...-4...-2...-1....1...-1....0....1....2...-1...-2
%e .-3....4....1....3....2...-1....0....0....3....0....3...-4....0....0....1...-3
%e ..2...-4....1....2....0....2....2...-3....1...-4....3....2....2....3....1...-3
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Jan 09 2011