A204215 Number of length 7 nonnegative integer arrays starting and ending with 0 with adjacent elements differing by no more than n.

51, 473, 2208, 7167, 18583, 41363, 82440, 151125, 259459, 422565, 659000, 991107, 1445367, 2052751, 2849072, 3875337, 5178099, 6809809, 8829168, 11301479, 14298999, 17901291, 22195576, 27277085, 33249411, 40224861, 48324808, 57680043

Offset

1,1

Comments

Row 6 of A204213.

Links

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

Formula

Empirical: a(n) = (44/15)*n^5 + (133/12)*n^4 + 17*n^3 + (161/12)*n^2 + (167/30)*n + 1.

Conjectures from Colin Barker, Jun 06 2018: (Start)

G.f.: x*(51 + 167*x + 135*x^2 - 6*x^3 + 6*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:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..3....1....3....3....5....5....4....2....4....4....4....0....4....1....0....3
..5....6....5....4....6....5....2....3....3....8....9....0....3....3....1....5
..4....4....3....3....6....7....4....6....5....7....7....3....6....4....5....5
..5....5....7....2....8....7....4....1....4....4....6....1....5....0....0....2
..3....1....5....0....3....5....0....1....0....0....4....5....2....2....3....1
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Cf. A204213.

Sequence in context: A273189 A222910 A259692 * A164646 A128511 A347922

Adjacent sequences: A204212 A204213 A204214 * A204216 A204217 A204218

Keyword

nonn

Author

R. H. Hardin, Jan 12 2012

Status

approved