A200194 Number of -n..n arrays x(0..4) of 5 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.

0, 24, 144, 506, 1298, 2794, 5300, 9220, 14974, 23094, 34120, 48712, 67524, 91346, 120950, 157254, 201146, 253672, 315838, 388820, 473738, 571896, 684534, 813084, 958900, 1123544, 1308488, 1515422, 1745934, 2001842, 2284852, 2596912, 2939842

Offset

1,2

Comments

Row 5 of A200192.

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^2*(12 + 48*x + 109*x^2 + 155*x^3 + 171*x^4 + 133*x^5 + 79*x^6 + 26*x^7 + 3*x^8) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, May 20 2018

Example

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

Crossrefs

Cf. A200192.

Sequence in context: A007900 A158874 A059593 * A182075 A054118 A223373

Adjacent sequences: A200191 A200192 A200193 * A200195 A200196 A200197

Keyword

nonn

Author

R. H. Hardin, Nov 14 2011

Status

approved