A212838 Number of 0..n arrays of length 5 with 0 never adjacent to n.

2, 99, 634, 2309, 6306, 14407, 29114, 53769, 92674, 151211, 235962, 354829, 517154, 733839, 1017466, 1382417, 1844994, 2423539, 3138554, 4012821, 5071522, 6342359, 7855674, 9644569, 11745026, 14196027, 17039674, 20321309, 24089634, 28396831

Offset

1,1

Comments

Row 4 of A212835.

Links

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

Formula

Empirical: a(n) = n^5 + 5*n^4 + 2*n^3 - 8*n^2 + n + 1.

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

G.f.: x*(2 + 87*x + 70*x^2 - 50*x^3 + 12*x^4 - x^5) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

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

Crossrefs

Cf. A212835.

Sequence in context: A223038 A324266 A258399 * A024241 A278684 A024242

Adjacent sequences: A212835 A212836 A212837 * A212839 A212840 A212841

Keyword

nonn

Author

R. H. Hardin, May 28 2012

Status

approved