A201043 Number of -n..n arrays of 4 elements with adjacent element differences also in -n..n.

41, 295, 1111, 3011, 6691, 13021, 23045, 37981, 59221, 88331, 127051, 177295, 241151, 320881, 418921, 537881, 680545, 849871, 1048991, 1281211, 1550011, 1859045, 2212141, 2613301, 3066701, 3576691, 4147795, 4784711, 5492311, 6275641

Offset

1,1

Comments

Row 4 of A201042.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (29/4)*n^4 + (29/2)*n^3 + (51/4)*n^2 + (11/2)*n + 1.

Conjectures from Colin Barker, May 21 2018: (Start)

G.f.: x*(41 + 90*x + 46*x^2 - 4*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

Some solutions for n=7:
..5...-5...-6...-2....2....3....1....5...-6...-3...-3....1....4...-2...-1...-1
.-1...-2...-3....3...-2...-2...-5...-1....0...-3....0....7...-3...-4...-5...-3
..2....2....4....2...-1...-5....1....1...-4....2...-1....2....2...-4...-2...-7
..1...-2....0....0....4....1....3...-1...-1....1....6...-4....6....2...-2...-1

Crossrefs

Cf. A201042.

Sequence in context: A167741 A074281 A090833 * A364269 A002646 A175110

Adjacent sequences: A201040 A201041 A201042 * A201044 A201045 A201046

Keyword

nonn

Author

R. H. Hardin, Nov 26 2011

Status

approved