A189581 Number of permutations of 1..n with displacements restricted to {-4,-3,0,1,2}.

1, 1, 1, 4, 13, 26, 48, 95, 205, 456, 974, 2024, 4225, 8930, 18977, 40199, 84815, 178867, 377753, 798542, 1687806, 3565554, 7531030, 15908857, 33611337, 71013181, 150026395, 316943191, 669573901, 1414567938, 2988489622, 6313604894

Offset: 1

Author

R. H. Hardin, Apr 24 2011

Keywords

• nonn

Examples

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

Links

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

Formula

Empirical: a(n) = a(n-1) +2*a(n-3) +3*a(n-4) +5*a(n-5) +5*a(n-6) -a(n-8) -6*a(n-9) -a(n-10) -3*a(n-11) -a(n-12) +a(n-13) +a(n-15).

Empirical g.f.: x*(1 + x^3 + 4*x^4 + 3*x^5 + x^6 - x^7 - 5*x^8 - x^9 - 3*x^10 - x^11 + x^12 + x^14) / (1 - x - 2*x^3 - 3*x^4 - 5*x^5 - 5*x^6 + x^8 + 6*x^9 + x^10 + 3*x^11 + x^12 - x^13 - x^15). - Colin Barker, May 02 2018