proposed

approved

editing

proposed

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

Row 6 of A205341.

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)

Some solutions for n=5:

Cf. A205341.

R. H. Hardin , Jan 26 2012

approved

editing

_R. H. Hardin (rhhardin(AT)att.net) _ Jan 26 2012

editing

approved

R. H. Hardin, <a href="/A205344/b205344.txt">Table of n, a(n) for n = 1..210</a>

allocated for Ron HardinNumber 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

1,1

Row 6 of A205341

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

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

allocated

nonn

R. H. Hardin (rhhardin(AT)att.net) Jan 26 2012

approved

editing

allocated for Ron Hardin

allocated

approved