A189602 Number of permutations of 1..n with displacements restricted to {-7,-6,-5,-4,-3,0,1,2}

1, 1, 1, 4, 13, 35, 89, 221, 499, 1146, 2755, 6750, 16570, 40293, 97355, 234629, 565632, 1365768, 3303221, 7992751, 19333657, 46743931, 112983171, 273083004, 660115058, 1595837810, 3858133501, 9327445000, 22549449187, 54512990509, 131783650621

Offset

1,4

Links

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

Formula

Empirical: a(n) = a(n-1) +2*a(n-3) +5*a(n-4) +9*a(n-5) +16*a(n-6) +29*a(n-7) +41*a(n-8) +45*a(n-9) +2*a(n-10) +5*a(n-11) -67*a(n-12) -55*a(n-13) -40*a(n-14) -31*a(n-15) -31*a(n-16) -63*a(n-17) -58*a(n-18) -31*a(n-19) -25*a(n-20) +14*a(n-21) +12*a(n-22) +5*a(n-23) +3*a(n-24) +3*a(n-25) +16*a(n-26) +12*a(n-27) +4*a(n-28) +5*a(n-29) -a(n-30) -a(n-35) -a(n-36)

Example

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

Crossrefs

Sequence in context: A210843 A177155 A189595 * A317781 A271358 A306349

Adjacent sequences: A189599 A189600 A189601 * A189603 A189604 A189605

Keyword

nonn

Author

R. H. Hardin Apr 24 2011

Status

approved