A201045 Number of -n..n arrays of 6 elements with adjacent element differences also in -n..n.

239, 4569, 33305, 148433, 491429, 1333683, 3139529, 6641881, 12930475, 23552717, 40627137, 66969449, 106231217, 163051127, 243218865, 353851601, 503583079, 702765313, 963682889, 1300779873, 1730899325, 2273535419, 2951098169

Offset

1,1

Comments

Row 6 of A201042.

Links

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

Formula

Empirical: a(n) = (2101/120)*n^6 + (2101/40)*n^5 + (1753/24)*n^4 + (1405/24)*n^3 + (569/20)*n^2 + (119/15)*n + 1.

Conjectures from Colin Barker, May 22 2018: (Start)

G.f.: x*(239 + 2896*x + 6341*x^2 + 2882*x^3 + 253*x^4 - 6*x^5 + x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Cf. A201042.

Sequence in context: A256377 A201194 A065750 * A056095 A224261 A223917

Adjacent sequences: A201042 A201043 A201044 * A201046 A201047 A201048

Keyword

nonn

Author

R. H. Hardin, Nov 26 2011

Status

approved