A268265 Number of length-(6+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

65, 717, 5492, 29461, 118530, 384605, 1061632, 2587557, 5717246, 11671405, 22326540, 40450997, 69992122, 116419581, 187129880, 291917125, 443515062, 658215437, 956567716, 1364165205, 1912522610, 2640050077, 3593128752

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^7 + n^6 + 6*n^5 + 5*n^4 + 20*n^3 + 12*n^2 + 20*n + 5 for n>1.

Conjectures from Colin Barker, Jan 13 2019: (Start)

G.f.: x*(65 + 197*x + 1576*x^2 + 1961*x^3 + 1016*x^4 + 271*x^5 - 76*x^6 + 35*x^7 - 5*x^8) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>9.

(End)

Example

Some solutions for n=5:
..3....2....1....5....2....4....2....5....1....5....2....2....1....4....0....5
..4....3....3....4....3....2....3....0....3....0....4....3....0....3....0....3
..0....5....5....5....1....3....0....0....1....0....3....4....1....1....4....2
..2....1....4....0....3....0....0....0....4....5....5....0....4....0....1....4
..0....3....1....4....0....3....5....0....1....3....0....2....0....1....1....5
..0....4....0....0....3....2....0....0....0....0....5....1....0....2....2....0
..2....1....0....5....1....0....1....5....0....2....4....3....0....5....1....1

Crossrefs

Row 6 of A268261.

Sequence in context: A224099 A220229 A200890 * A353939 A351269 A088677

Adjacent sequences: A268262 A268263 A268264 * A268266 A268267 A268268

Keyword

nonn

Author

R. H. Hardin, Jan 29 2016

Status

approved