A189590 Number of permutations of 1..n with displacements restricted to {-5,-4,-2,0,1,3}

1, 1, 2, 4, 13, 35, 93, 227, 499, 1185, 2823, 6809, 16640, 40117, 96797, 232099, 556269, 1338482, 3218538, 7747725, 18645571, 44845905, 107873385, 259405282, 623911219, 1500766461, 3609839279, 8683275206, 20886151010, 50237661120, 120837419260

Offset

1,3

Links

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

Formula

Empirical: a(n) = a(n-1) +2*a(n-3) +4*a(n-4) +12*a(n-5) +8*a(n-6) +36*a(n-7) +52*a(n-8) -2*a(n-9) +67*a(n-10) -5*a(n-11) -64*a(n-12) -16*a(n-13) -46*a(n-14) -29*a(n-15) -127*a(n-16) -14*a(n-17) -174*a(n-18) -70*a(n-19) +187*a(n-20) -59*a(n-21) +52*a(n-22) -24*a(n-23) +88*a(n-24) -168*a(n-25) +74*a(n-26) +320*a(n-27) -82*a(n-28) -66*a(n-29) -284*a(n-30) +46*a(n-31) +32*a(n-32) +230*a(n-33) +2*a(n-34) -203*a(n-35) +39*a(n-36) +8*a(n-37) +156*a(n-38) -42*a(n-39) +68*a(n-40) -88*a(n-41) +16*a(n-42) -24*a(n-43) +14*a(n-44) +a(n-45) -9*a(n-46) -12*a(n-47) -16*a(n-48) +10*a(n-49) +a(n-50) +3*a(n-51) -2*a(n-52) +a(n-55) +a(n-56)

Example

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

Crossrefs

Sequence in context: A148234 A284335 A192443 * A189597 A148235 A151522

Adjacent sequences: A189587 A189588 A189589 * A189591 A189592 A189593

Keyword

nonn

Author

R. H. Hardin Apr 24 2011

Status

approved