A204214 Number of length 6 nonnegative integer arrays starting and ending with 0 with adjacent elements differing by no more than n.

21, 120, 404, 1025, 2181, 4116, 7120, 11529, 17725, 26136, 37236, 51545, 69629, 92100, 119616, 152881, 192645, 239704, 294900, 359121, 433301, 518420, 615504, 725625, 849901, 989496, 1145620, 1319529, 1512525, 1725956, 1961216, 2219745

Offset

1,1

Comments

Row 5 of A204213.

Links

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

Formula

Empirical: a(n) = (23/12)*n^4 + (37/6)*n^3 + (91/12)*n^2 + (13/3)*n + 1.

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

G.f.: x*(21 + 15*x + 14*x^2 - 5*x^3 + x^4) / (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
..4....0....2....2....0....5....0....3....5....0....4....5....4....1....1....3
..1....4....2....2....3....2....2....6....1....5....8...10....8....2....3....5
..4....3....7....1....2....0....3....5....5....4....6...10....3....6....3....6
..2....4....5....3....4....3....0....5....2....5....3....5....4....2....4....3
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0

Crossrefs

Cf. A204213.

Sequence in context: A079417 A267877 A183318 * A074088 A245031 A316713

Adjacent sequences: A204211 A204212 A204213 * A204215 A204216 A204217

Keyword

nonn

Author

R. H. Hardin, Jan 12 2012

Status

approved