A199849 Number of -n..n arrays x(0..4) of 5 elements with zero sum and no element more than one greater than the previous.

26, 66, 132, 239, 399, 630, 944, 1367, 1913, 2612, 3482, 4557, 5857, 7424, 9278, 11465, 14011, 16966, 20356, 24239, 28643, 33630, 39232, 45515, 52513, 60300, 68910, 78421, 88873, 100348, 112886, 126577, 141463, 157638, 175148, 194091, 214515, 236526

Offset

1,1

Comments

Row 5 of A199847.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) -a(n-3) -2*a(n-5) +2*a(n-6) +a(n-8) -2*a(n-10) +a(n-11) for n>12.

Empirical g.f.: x*(26 + 14*x + x^3 - 13*x^4 + 16*x^5 + 3*x^6 + 10*x^7 - 3*x^8 - 16*x^9 + 7*x^10 + x^11) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, May 16 2018

Example

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

Crossrefs

Cf. A199847.

Sequence in context: A250605 A020155 A063304 * A116300 A299798 A039377

Adjacent sequences: A199846 A199847 A199848 * A199850 A199851 A199852

Keyword

nonn

Author

R. H. Hardin, Nov 11 2011

Status

approved