A221464 Number of 0..n arrays of length 5 with each element unequal to at least one neighbor, starting with 0.

3, 32, 135, 384, 875, 1728, 3087, 5120, 8019, 12000, 17303, 24192, 32955, 43904, 57375, 73728, 93347, 116640, 144039, 176000, 213003, 255552, 304175, 359424, 421875, 492128, 570807, 658560, 756059, 864000, 983103, 1114112, 1257795

Offset

1,1

Comments

Row 5 of A221463.

Links

R. H. Hardin, Table of n, a(n) for n = 1..137

Formula

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

Conjectures from Colin Barker, Aug 05 2018: (Start)

G.f.: x*(3 + 17*x + 5*x^2 - x^3) / (1 - x)^5.

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>5.

(End)

Example

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

Crossrefs

Cf. A221463.

Sequence in context: A345687 A211224 A213845 * A119940 A004256 A183457

Adjacent sequences: A221461 A221462 A221463 * A221465 A221466 A221467

Keyword

nonn

Author

R. H. Hardin, Jan 17 2013

Status

approved