A201044 Number of -n..n arrays of 5 elements with adjacent element differences also in -n..n.

99, 1161, 6083, 21141, 57343, 131781, 268983, 502265, 875083, 1442385, 2271963, 3445805, 5061447, 7233325, 10094127, 13796145, 18512627, 24439129, 31794867, 40824069, 51797327, 65012949, 80798311, 99511209, 121541211, 147311009

Offset

1,1

Comments

Row 5 of A201042.

Links

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

Formula

Empirical: a(n) = (169/15)*n^5 + (169/6)*n^4 + 32*n^3 + (119/6)*n^2 + (101/15)*n + 1.

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

G.f.: x*(99 + 567*x + 602*x^2 + 78*x^3 + 7*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Cf. A201042.

Sequence in context: A074786 A249335 A338258 * A196577 A259693 A196785

Adjacent sequences: A201041 A201042 A201043 * A201045 A201046 A201047

Keyword

nonn

Author

R. H. Hardin, Nov 26 2011

Status

approved