A201046 Number of -n..n arrays of 7 elements with adjacent element differences also in -n..n.

577, 17981, 182349, 1042167, 4211559, 13497523, 36644243, 87831605, 191065045, 384593857, 726495089, 1301560155, 2229621291, 3675454983, 5860399495, 9075823625, 13698583817, 20208606757, 29208734581, 41446969823, 57841257231

Offset

1,1

Comments

Row 7 of A201042.

Links

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

Formula

Empirical: a(n) = (17141/630)*n^7 + (17141/180)*n^6 + (28177/180)*n^5 + (2759/18)*n^4 + (17299/180)*n^3 + (6929/180)*n^2 + (1921/210)*n + 1.

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

G.f.: x*(577 + 13365*x + 54657*x^2 + 54531*x^3 + 13449*x^4 + 541*x^5 + 9*x^6 - x^7) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

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

Crossrefs

Cf. A201042.

Sequence in context: A101249 A202011 A157264 * A154511 A221331 A163042

Adjacent sequences: A201043 A201044 A201045 * A201047 A201048 A201049

Keyword

nonn

Author

R. H. Hardin, Nov 26 2011

Status

approved