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

Author

R. H. Hardin, Jan 29 2016

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Row 5 of A268261.

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)