A205344 Number of length 7 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than n.

5, 93, 689, 2912, 8927, 22297, 48335, 94456, 170529, 289229, 466389, 721352, 1077323, 1561721, 2206531, 3048656, 4130269, 5499165, 7209113, 9320208, 11899223, 15019961, 18763607, 23219080, 28483385, 34661965, 41869053, 50228024

Offset

1,1

Comments

Row 6 of A205341.

Links

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

Formula

Empirical: a(n) = (44/15)*n^5 - (5/12)*n^4 + (5/12)*n^2 + (31/15)*n.

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

G.f.: x*(5 + 63*x + 206*x^2 + 73*x^3 + 5*x^4) / (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:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....5....3....5....1....1....5....4....3....5....4....5....1....3....4
..6....4...10....6....0....2....4....3....8....6...10....3....8....5....1....7
..8....1....5....1....2....0....8....6....7....5....6....6....7....1....5....6
..7....4....3....5....4....4....6....5....3....3....2....7....5....5....3....7
..4....3....5....2....1....3....1....2....2....1....4....5....1....2....2....3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Cf. A205341.

Sequence in context: A024069 A295407 A152283 * A270408 A000365 A209471

Adjacent sequences: A205341 A205342 A205343 * A205345 A205346 A205347

Keyword

nonn

Author

R. H. Hardin, Jan 26 2012

Status

approved