A205343 Number of length 6 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than n.

0, 24, 138, 454, 1130, 2370, 4424, 7588, 12204, 18660, 27390, 38874, 53638, 72254, 95340, 123560, 157624, 198288, 246354, 302670, 368130, 443674, 530288, 629004, 740900, 867100, 1008774, 1167138, 1343454, 1539030, 1755220, 1993424, 2255088

Offset

1,2

Comments

Row 5 of A205341.

Links

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

Formula

Empirical: a(n) = (23/12)*n^4 - (1/2)*n^3 + (1/12)*n^2 - (3/2)*n.

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

G.f.: 2*x^2*(12 + 9*x + 2*x^2) / (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=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..5....4....3....4....2....4....3....5....5....3....5....4....5....1....1....1
..1....2....2....9....5....7....6....6....2....6....0....2....2....0....6....5
..5....0....5....8....1....3....7....8....6....4....5....0....1....2....9....9
..3....4....1....5....5....1....2....4....2....5....2....1....5....1....5....4
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Cf. A205341.

Sequence in context: A093699 A275405 A223409 * A267631 A305681 A199827

Adjacent sequences: A205340 A205341 A205342 * A205344 A205345 A205346

Keyword

nonn

Author

R. H. Hardin, Jan 26 2012

Status

approved