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

Author

R. H. Hardin, Jan 29 2016

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 3 of A268261.

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)