A189593 Number of permutations of 1..n with displacements restricted to {-6,-5,-4,-3,-2,0,1}.

1, 1, 2, 4, 7, 12, 21, 36, 62, 108, 188, 326, 565, 980, 1700, 2949, 5116, 8875, 15395, 26705, 46325, 80360, 139400, 241816, 419476, 727661, 1262267, 2189644, 3798357, 6588977, 11429841, 19827246, 34394152, 59663238, 103497303, 179535876

Offset

1,3

Comments

a(n+1) is the number of multus bitstrings of length n with no runs of 7 ones. - Steven Finch, Mar 25 2020

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Steven Finch, Cantor-solus and Cantor-multus distributions, arXiv:2003.09458 [math.CO], 2020.

Formula

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

Empirical g.f.: x*(1 + x^2)*(1 + x^3 + x^4) / ((1 - x + x^2)*(1 - x^2 - 2*x^3 - 2*x^4 - x^5)). - Colin Barker, May 02 2018

Example

Some solutions for n=14:
..1....4....3....1....4....5....1....1....3....1....1....4....1....1....1....3
..5....1....1....5....1....1....5....7....1....2....2....1....5....4....7....1
..2....2....2....2....2....2....2....2....2....5....7....2....2....2....2....2
..3....3....4....3....3....3....3....3....4....3....3....3....3....3....3....4
..4....8....7....4....5....4....4....4...10....4....4....5....4....5....4....7
..6....5....5....6....6....6...11....5....5....8....5...10....6....9....5....5
..7....6....6...10....7....7....6....6....6....6....6....6...11....6....6....6
.10....7...10....7....8...11....7....8....7....7....8....7....7....7....8...12
..8....9....8....8...13....8....8....9....8...13....9....8....8....8....9....8
..9...14....9....9....9....9....9...10....9....9...14....9....9...14...12....9
.13...10...11...11...10...10...10...11...14...10...10...11...10...10...10...10
.11...11...14...14...11...14...14...14...11...11...11...12...12...11...11...11
.12...12...12...12...12...12...12...12...12...12...12...13...13...12...13...13
.14...13...13...13...14...13...13...13...13...14...13...14...14...13...14...14

Crossrefs

Sequence in context: A357947 A227376 A245531 * A100671 A189600 A005251

Adjacent sequences: A189590 A189591 A189592 * A189594 A189595 A189596

Keyword

nonn

Author

R. H. Hardin, Apr 24 2011

Status

approved