A212841 Number of 0..n arrays of length 8 with 0 never adjacent to n.

2, 1393, 28642, 231521, 1168786, 4414417, 13667858, 36590017, 87627106, 192124721, 392074882, 753879073, 1378550642, 2414820241, 4075648306, 6658688897, 10571289538, 16360652017, 24749819426, 36680195041, 53361338962

Offset: 1

Author

R. H. Hardin, May 28 2012

Keywords

• nonn

Comments

Row 7 of A212835.

Examples

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

Links

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

Crossrefs

Cf. A212835.

Formula

Empirical: a(n) = n^8 + 8*n^7 + 14*n^6 - 16*n^5 - 30*n^4 + 24*n^3 + 8*n^2 - 8*n + 1.

Conjectures from Colin Barker, Jul 21 2018: (Start)

G.f.: x*(2 + 1375*x + 16177*x^2 + 23723*x^3 - 551*x^4 - 563*x^5 + 179*x^6 - 23*x^7 + x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)