A199707 Number of -n..n arrays x(0..4) of 5 elements with zero sum and no two neighbors equal.

14, 200, 892, 2734, 6504, 13324, 24394, 41344, 65788, 99858, 145596, 205612, 282386, 379036, 498440, 644218, 819692, 1028960, 1275766, 1564716, 1899968, 2286630, 2729288, 3233528, 3804374, 4447920, 5169588, 5975974, 6872944, 7867572, 8966146

Offset

1,1

Comments

Row 5 of A199704.

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).

Empirical g.f.: 2*x*(7 + 86*x + 246*x^2 + 482*x^3 + 618*x^4 + 618*x^5 + 426*x^6 + 222*x^7 + 47*x^8 + 8*x^9) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, May 16 2018

Example

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

Crossrefs

Cf. A199704.

Sequence in context: A124239 A041366 A051817 * A222586 A221830 A068769

Adjacent sequences: A199704 A199705 A199706 * A199708 A199709 A199710

Keyword

nonn

Author

R. H. Hardin, Nov 09 2011

Status

approved