A203296 - OEIS

%I #5 Mar 31 2012 12:36:56

%S 7,28,176,944,4206,15798,51768,151393,403131,991692,2280620,4948566,

%T 10208256,20143302,38215998,70007951,124283183,214475760,360744276,

%U 592751998,953388836,1503671490,2329136950,3548069499,5322005825

%N Number of arrays of 12 nondecreasing integers in -n..n with sum zero and equal numbers greater than zero and less than zero

%C Row 6 of A203291

%H R. H. Hardin, <a href="/A203296/b203296.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) +a(n-4) -a(n-5) +3*a(n-6) -a(n-7) +5*a(n-8) -a(n-9) -6*a(n-10) -2*a(n-11) -a(n-12) +a(n-13) +a(n-14) +13*a(n-15) -4*a(n-16) -2*a(n-17) -4*a(n-18) -4*a(n-19) -2*a(n-20) -4*a(n-21) +13*a(n-22) +a(n-23) +a(n-24) -a(n-25) -2*a(n-26) -6*a(n-27) -a(n-28) +5*a(n-29) -a(n-30) +3*a(n-31) -a(n-32) +a(n-33) -3*a(n-34) -a(n-35) +3*a(n-36) -a(n-37)

%e Some solutions for n=3

%e .-3...-3...-2...-3...-3...-3...-3...-3...-2...-3...-3...-3...-3...-3...-2...-3

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

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

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

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

%e ..0...-1...-1....0....0....0....0....0....0...-1....0...-1...-1....0...-1....0

%e ..0....2....1....0....0....0....0....0....0....1....0....1....1....0....1....0

%e ..0....2....2....1....1....1....2....0....1....1....0....2....1....0....1....2

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

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

%e ..2....2....2....3....2....3....2....2....1....2....3....2....3....3....1....2

%e ..2....2....2....3....2....3....3....2....2....2....3....3....3....3....3....2

%K nonn

%O 1,1

%A _R. H. Hardin_ Dec 31 2011