A221526 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by 2 or more.

0, 10, 274, 2172, 9982, 33380, 90684, 212812, 447962, 867012, 1569640, 2691164, 4410102, 6956452, 10620692, 15763500, 22826194, 32341892, 44947392, 61395772, 82569710, 109495524, 143357932, 185515532, 237517002, 301118020, 378298904

Offset

1,2

Comments

Row 6 of A221524.

Links

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

Formula

Empirical: a(n) = 1*n^6 - 20*n^4 + 83*n^3 - 182*n^2 + 236*n - 148 for n>3.

Conjectures from Colin Barker, Aug 06 2018: (Start)

G.f.: 2*x^2*(5 + 102*x + 232*x^2 + 91*x^3 - 61*x^4 + 3*x^5 - 15*x^6 + 4*x^7 - x^8) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>10.

(End)

Example

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

Crossrefs

Cf. A221524.

Sequence in context: A055055 A222998 A368770 * A153331 A290202 A203149

Adjacent sequences: A221523 A221524 A221525 * A221527 A221528 A221529

Keyword

nonn

Author

R. H. Hardin, Jan 19 2013

Status

approved