A268262 Number of length-(3+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.

9, 42, 143, 378, 837, 1634, 2907, 4818, 7553, 11322, 16359, 22922, 31293, 41778, 54707, 70434, 89337, 111818, 138303, 169242, 205109, 246402, 293643, 347378, 408177, 476634, 553367, 639018, 734253, 839762, 956259, 1084482, 1225193

Offset

1,1

Links

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

Formula

Empirical: a(n) = n^4 + n^3 + 3*n^2 + 2*n + 2.

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

G.f.: x*(9 - 3*x + 23*x^2 - 7*x^3 + 2*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=8:
..0....2....4....3....2....2....5....1....7....2....4....8....4....2....4....7
..2....4....0....6....4....1....0....6....0....8....1....3....2....4....1....6
..8....6....0....8....0....5....0....4....3....0....6....7....7....0....3....2
..5....7....2....4....3....1....4....5....1....1....8....0....4....4....8....7

Crossrefs

Row 3 of A268261.

Sequence in context: A292481 A051923 A180670 * A293101 A084899 A268622

Adjacent sequences: A268259 A268260 A268261 * A268263 A268264 A268265

Keyword

nonn

Author

R. H. Hardin, Jan 29 2016

Status

approved