A205345 Number of length 8 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than n.

0, 272, 3272, 18652, 71630, 214724, 542850, 1211784, 2459988, 4633800, 8215988, 13857668, 22413586, 34980764, 52940510, 78003792, 112259976, 158228928, 218916480, 297873260, 399256886, 527897524, 689366810, 890050136, 1137222300

Offset

1,2

Comments

Row 7 of A205341.

Links

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

Formula

Empirical: a(n) = (841/180)*n^6 - (1/3)*n^5 - (19/36)*n^4 + (1/3)*n^3 - (103/90)*n^2 - 3*n.

Conjectures from Colin Barker, Jun 11 2018: (Start)

G.f.: 2*x^2*(136 + 684*x + 730*x^2 + 129*x^3 + 3*x^4) / (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=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..5....3....5....2....2....2....2....3....5....3....1....2....4....2....3....4
..6....7....8....6....3....4....4....4....9....5....2....5....8....6....5....7
..7....8...11....7....4....3....2....7...12....1....0....4....7....4....6....8
.10....4....9....6....3....6....7....3....7....2....4....3....3....8....3....7
..6....5....4....4....0....5....3....6....3....7....6....0....1....3....1....8
..5....3....2....3....3....4....4....2....5....2....5....2....5....5....3....3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Cf. A205341.

Sequence in context: A305952 A317213 A178268 * A302899 A266106 A264077

Adjacent sequences: A205342 A205343 A205344 * A205346 A205347 A205348

Keyword

nonn

Author

R. H. Hardin, Jan 26 2012

Status

approved