A199850 Number of -n..n arrays x(0..5) of 6 elements with zero sum and no element more than one greater than the previous.

63, 192, 428, 845, 1532, 2600, 4188, 6465, 9634, 13932, 19636, 27065, 36582, 48598, 63576, 82029, 104530, 131710, 164262, 202945, 248586, 302082, 364406, 436607, 519814, 615238, 724178, 848019, 988240, 1146414, 1324210, 1523399, 1745856

Offset: 1

Author

R. H. Hardin, Nov 11 2011

Keywords

• nonn

Comments

Row 6 of A199847.

Examples

			Some solutions for n=6:
..5....6....5....5....2....1....3....2....3....1....2....4....4....4....2....5
..4...-2....6....0....3....2....1....3....3...-1....0....2....4....3....3....0
..2...-1....1...-1....3....3...-2....2....3...-1....1....0....2....2....0....1
.-4....0...-1....0....1....0...-1....0...-2....0....2....0...-4...-2...-2...-1
.-3....0...-6...-2...-3...-3....0...-4...-2....1....0...-1...-3...-2...-1...-1
.-4...-3...-5...-2...-6...-3...-1...-3...-5....0...-5...-5...-3...-5...-2...-4
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A199847.

Formula

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.

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