A263661 Number of length n arrays of permutations of 0..n-1 with each element moved by -3 to 3 places and with no two consecutive increases or two consecutive decreases.

1, 2, 4, 10, 22, 40, 70, 133, 254, 482, 902, 1710, 3214, 6094, 11446, 21702, 40766, 77294, 145190, 275286, 517102, 980446, 1841686, 3491910, 6559262, 12436622, 23361158, 44293686, 83201998, 157754302, 296328310, 561850278, 1055388926

Offset

1,2

Links

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

Formula

Empirical: a(n) = 3*a(n-2) + 2*a(n-4) for n>12.

Empirical g.f.: x*(1 + x)*(1 + x + 4*x^3 + 4*x^4 + 2*x^5 - 6*x^6 - x^7 + x^8 + 2*x^9 - 2*x^10) / (1 - 3*x^2 - 2*x^4). - Colin Barker, Jan 02 2019

Example

Some solutions for n=7:
..3....1....3....2....1....2....0....1....2....1....3....1....0....3....2....1
..1....3....0....1....3....4....2....0....0....2....1....0....4....1....1....4
..5....0....2....4....0....0....1....4....5....0....4....5....1....2....3....0
..0....5....1....0....4....3....6....2....1....4....0....3....3....0....0....3
..4....2....5....6....2....1....3....6....4....3....5....4....2....5....5....2
..2....6....4....3....6....6....5....3....3....6....2....2....6....4....4....6
..6....4....6....5....5....5....4....5....6....5....6....6....5....6....6....5

Crossrefs

Column 3 of A263666.

Sequence in context: A036954 A109679 A023036 * A005306 A075898 A360631

Adjacent sequences: A263658 A263659 A263660 * A263662 A263663 A263664

Keyword

nonn

Author

R. H. Hardin, Oct 23 2015

Status

approved