A188213 - OEIS

%I #8 Apr 27 2018 08:18:13

%S 338,676,1242,2137,3486,5444,8196,11963,17002,23612,32134,42955,56512,

%T 73294,93844,118765,148718,184430,226694,276373,334402,401792,479632,

%U 569093,671430,787986,920192,1069575,1237756,1426456,1637498,1872809

%N Number of nondecreasing arrangements of 6 numbers in -(n+4)..(n+4) with sum zero.

%C Row 6 of A188211.

%H R. H. Hardin, <a href="/A188213/b188213.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + 2*a(n-5) - a(n-6) - a(n-7) + 2*a(n-8) - a(n-10) - 2*a(n-11) + 3*a(n-12) - a(n-13).

%F Empirical g.f.: x*(338 - 338*x - 110*x^2 + 101*x^3 + 235*x^4 - 174*x^5 - 41*x^6 + 279*x^7 - 83*x^8 - 217*x^9 - 146*x^10 + 395*x^11 - 151*x^12) / ((1 - x)^6*(1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, Apr 27 2018

%e Some solutions for n=3:

%e .-3...-6...-6...-4...-6...-4...-5...-4...-5...-5...-4...-6...-4...-4...-6...-3

%e .-3...-2...-2...-3...-6...-2...-2...-3...-5...-4...-4...-5...-1...-3...-4...-3

%e .-3...-2...-1...-2...-5...-1...-2...-1...-2....0....0...-3...-1....0....0...-2

%e .-3....0....0...-2....5....0...-2...-1....3....2....0....4....0....2....0...-1

%e ..5....4....3....4....6....3....4....4....4....2....4....4....2....2....5....3

%e ..7....6....6....7....6....4....7....5....5....5....4....6....4....3....5....6

%Y Cf. A188211.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 24 2011