A221574 Number of 0..n arrays of length 3 with each element differing from at least one neighbor by something other than 1.

2, 9, 26, 59, 114, 197, 314, 471, 674, 929, 1242, 1619, 2066, 2589, 3194, 3887, 4674, 5561, 6554, 7659, 8882, 10229, 11706, 13319, 15074, 16977, 19034, 21251, 23634, 26189, 28922, 31839, 34946, 38249, 41754, 45467, 49394, 53541, 57914, 62519, 67362

Offset

1,1

Comments

Row 3 of A221573.

Links

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

Formula

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

Conjectures from Colin Barker, Aug 08 2018: (Start)

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

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

(End)

Example

Some solutions for n=6:
..1....0....5....2....5....0....6....6....6....0....6....0....1....1....6....5
..6....5....1....4....3....5....4....6....4....4....1....4....1....3....2....1
..4....5....1....4....1....2....0....4....2....0....6....4....3....0....5....5

Crossrefs

Cf. A221573.

Sequence in context: A218460 A085070 A083383 * A082289 A014150 A213387

Adjacent sequences: A221571 A221572 A221573 * A221575 A221576 A221577

Keyword

nonn

Author

R. H. Hardin, Jan 20 2013

Status

approved