|
%I #7 Dec 15 2023 20:06:34
%S 5,15,57,188,544,1380,3172,6687,13163,24435,43195,73194,119616,189346,
%T 291486,437723,642977,925889,1309647,1822576,2499166,3380806,4517000,
%U 5966265,7797585,10091447,12941561,16456084,20759580,25994452,32323204
%N Number of arrays of 8 nondecreasing integers in -n..n with sum zero and equal numbers greater than zero and less than zero.
%C Row 4 of A203291.
%H R. H. Hardin, <a href="/A203294/b203294.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +7*a(n-6) -3*a(n-7) -2*a(n-8) -2*a(n-9) -3*a(n-10) +7*a(n-11) -3*a(n-14) -a(n-15) +3*a(n-16) -a(n-17).
%e Some solutions for n=3
%e .-3....0...-3...-3...-3...-2...-3...-3...-3...-3...-2...-1...-3...-3...-3...-2
%e .-3....0....0...-3...-2....0...-2...-3...-3...-3...-2...-1...-2...-1...-3...-2
%e .-2....0....0...-3...-2....0...-1...-2...-1....0...-2...-1...-2....0...-3...-1
%e .-1....0....0....0...-1....0...-1...-2...-1....0....0....0....0....0...-3...-1
%e ..1....0....0....0....1....0....1....2....2....0....0....0....0....0....3....1
%e ..2....0....0....3....2....0....1....2....2....0....2....1....1....0....3....1
%e ..3....0....0....3....2....0....2....3....2....3....2....1....3....1....3....1
%e ..3....0....3....3....3....2....3....3....2....3....2....1....3....3....3....3
%Y Cf. A203291.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 31 2011
| 