A212836 Number of 0..n arrays of length 3 with 0 never adjacent to n.

2, 17, 50, 107, 194, 317, 482, 695, 962, 1289, 1682, 2147, 2690, 3317, 4034, 4847, 5762, 6785, 7922, 9179, 10562, 12077, 13730, 15527, 17474, 19577, 21842, 24275, 26882, 29669, 32642, 35807, 39170, 42737, 46514, 50507, 54722, 59165, 63842, 68759, 73922

Offset: 1

Author

R. H. Hardin, May 28 2012

Keywords

• nonn

Comments

Row 2 of A212835.

Examples

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

Links

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

Crossrefs

Cf. A212835.

Formula

Empirical: a(n) = n^3 + 3*n^2 - n - 1.

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

G.f.: x*(2 + 9*x - 6*x^2 + x^3) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)