A199850 - OEIS

%I #10 May 16 2018 16:34:43

%S 63,192,428,845,1532,2600,4188,6465,9634,13932,19636,27065,36582,

%T 48598,63576,82029,104530,131710,164262,202945,248586,302082,364406,

%U 436607,519814,615238,724178,848019,988240,1146414,1324210,1523399,1745856

%N Number of -n..n arrays x(0..5) of 6 elements with zero sum and no element more than one greater than the previous.

%C Row 6 of A199847.

%H R. H. Hardin, <a href="/A199850/b199850.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) for n>14.

%F Empirical g.f.: x*(63 + 3*x - 22*x^2 + 8*x^3 + 45*x^4 - 4*x^5 - 24*x^6 + 32*x^7 + 19*x^8 - 27*x^9 - 43*x^10 + 39*x^11 + 8*x^12 - 9*x^13) / ((1 - x)^6*(1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - _Colin Barker_, May 16 2018

%e Some solutions for n=6:

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

%e ..4...-2....6....0....3....2....1....3....3...-1....0....2....4....3....3....0

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

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

%e .-3....0...-6...-2...-3...-3....0...-4...-2....1....0...-1...-3...-2...-1...-1

%e .-4...-3...-5...-2...-6...-3...-1...-3...-5....0...-5...-5...-3...-5...-2...-4

%Y Cf. A199847.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 11 2011