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A204215
Number of length 7 nonnegative integer arrays starting and ending with 0 with adjacent elements differing by no more than n.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jan 12 2012
STATUS
approved