A268264 Number of length-(5+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

33, 273, 1616, 6877, 22710, 62249, 148468, 318261, 627242, 1155265, 2012664, 3347213, 5351806, 8272857, 12419420, 18173029, 25998258, 36454001, 50205472, 68036925, 90865094, 119753353, 155926596, 200786837, 255929530, 323160609

Offset

1,1

Links

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

Formula

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

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

G.f.: x*(33 + 42*x + 398*x^2 + 143*x^3 + 107*x^4 - 2*x^5 - 2*x^6 + x^7) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>8.

(End)

Example

Some solutions for n=7:
..6....0....4....7....2....6....4....6....5....0....7....0....5....7....1....3
..3....6....1....2....4....0....6....1....0....2....0....0....2....3....2....2
..2....7....7....3....6....3....7....0....0....7....7....2....4....6....3....5
..6....0....0....6....3....0....2....4....6....5....6....1....3....3....5....7
..0....0....5....2....2....4....5....5....1....4....4....0....4....7....3....6
..3....4....6....0....0....1....7....1....3....5....0....4....2....2....2....3

Crossrefs

Row 5 of A268261.

Sequence in context: A061223 A119782 A252978 * A008515 A179995 A000539

Adjacent sequences: A268261 A268262 A268263 * A268265 A268266 A268267

Keyword

nonn

Author

R. H. Hardin, Jan 29 2016

Status

approved