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

Author

R. H. Hardin, Oct 24 2015

Keywords

• nonn

Examples

			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
		

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.

Crossrefs

Column 1 of A263714.

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