A200195 Number of -n..n arrays x(0..5) of 6 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

2, 54, 482, 2240, 7266, 18838, 41938, 83600, 153278, 263198, 428718, 668684, 1005790, 1466934, 2083578, 2892104, 3934174, 5257082, 6914122, 8964936, 11475878, 14520370, 18179258, 22541172, 27702886, 33769670, 40855654, 49084180

Offset

1,1

Comments

Row 6 of A200192.

Links

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

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).

Empirical g.f.: 2*x*(1 + 24*x + 162*x^2 + 452*x^3 + 782*x^4 + 999*x^5 + 1045*x^6 + 910*x^7 + 622*x^8 + 292*x^9 + 74*x^10 + 5*x^11) / ((1 - x)^6*(1 + x)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 20 2018

Example

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

Crossrefs

Cf. A200192.

Sequence in context: A078691 A280754 A113028 * A202739 A055024 A057411

Adjacent sequences: A200192 A200193 A200194 * A200196 A200197 A200198

Keyword

nonn

Author

R. H. Hardin, Nov 14 2011

Status

approved