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

1,1

Comments

Row 2 of A212835.

Links

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

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)

Example

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

Crossrefs

Cf. A212835.

Sequence in context: A105691 A360416 A192345 * A338564 A125609 A100518

Adjacent sequences: A212833 A212834 A212835 * A212837 A212838 A212839

Keyword

nonn

Author

R. H. Hardin, May 28 2012

Status

approved