A263710 Number of length n arrays of permutations of 0..n-1 with each element moved by -1 to 1 places and every four consecutive elements having its maximum within 4 of its minimum.

1, 2, 3, 5, 8, 11, 17, 25, 37, 57, 84, 127, 191, 284, 429, 641, 961, 1445, 2161, 3246, 4867, 7293, 10948, 16407, 24609, 36913, 55337, 83009, 124472, 186655, 279951, 419784, 629561, 944129, 1415809, 2123305, 3184145, 4775114, 7161091, 10738981, 16104880

Offset

1,2

Links

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

Michael A. Allen, Combinations without specified separations and restricted-overlap tiling with combs, arXiv:2210.08167 [math.CO], 2022.

Formula

Empirical: a(n) = a(n-1) + a(n-3) - a(n-4) + 2*a(n-5) - a(n-6) + a(n-7).

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

Example

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

Crossrefs

Column 1 of A263714.

Sequence in context: A091498 A227562 A000511 * A135908 A056891 A065462

Adjacent sequences: A263707 A263708 A263709 * A263711 A263712 A263713

Keyword

nonn

Author

R. H. Hardin, Oct 24 2015

Status

approved