A212837 Number of 0..n arrays of length 4 with 0 never adjacent to n.

2, 41, 178, 497, 1106, 2137, 3746, 6113, 9442, 13961, 19922, 27601, 37298, 49337, 64066, 81857, 103106, 128233, 157682, 191921, 231442, 276761, 328418, 386977, 453026, 527177, 610066, 702353, 804722, 917881, 1042562, 1179521, 1329538

Offset

1,1

Comments

Row 3 of A212835.

Links

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

Formula

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

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

G.f.: x*(2 + 31*x - 7*x^2 - 3*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

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

Crossrefs

Cf. A212835.

Sequence in context: A088565 A090195 A287335 * A063271 A142160 A174615

Adjacent sequences: A212834 A212835 A212836 * A212838 A212839 A212840

Keyword

nonn

Author

R. H. Hardin, May 28 2012

Status

approved