A189592 Number of permutations of 1..n with displacements restricted to {-5,-4,0,1,2,3}

1, 1, 1, 1, 8, 35, 107, 247, 535, 1223, 3009, 8033, 21789, 56561, 141754, 352916, 885060, 2243639, 5731032, 14652087, 37302363, 94594125, 239640285, 607680601, 1543064845, 3921438808, 9965699656, 25314407628, 64275368601, 163181158704

Offset

1,5

Links

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

Formula

Empirical: a(n) = a(n-1) +3*a(n-3) +5*a(n-4) +9*a(n-5) +26*a(n-6) +63*a(n-7) +61*a(n-8) +4*a(n-9) -16*a(n-10) -125*a(n-11) -57*a(n-12) -33*a(n-13) -350*a(n-14) -394*a(n-15) -162*a(n-16) -303*a(n-17) +44*a(n-18) +67*a(n-19) -52*a(n-20) -96*a(n-21) +15*a(n-22) +285*a(n-23) -48*a(n-24) -49*a(n-25) +195*a(n-26) -485*a(n-27) +428*a(n-28) -165*a(n-29) +39*a(n-30) +88*a(n-31) -134*a(n-32) +111*a(n-33) +117*a(n-34) +96*a(n-35) +47*a(n-36) +26*a(n-37) +19*a(n-38) -2*a(n-39) +48*a(n-40) -26*a(n-41) +2*a(n-42) -43*a(n-43) +8*a(n-44) -36*a(n-45) +3*a(n-46) -a(n-47) -15*a(n-48) +6*a(n-49) -5*a(n-50) +4*a(n-51) -a(n-52) +2*a(n-53) +a(n-56)

Example

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

Crossrefs

Sequence in context: A058102 A212674 A279743 * A285737 A244882 A006600

Adjacent sequences: A189589 A189590 A189591 * A189593 A189594 A189595

Keyword

nonn

Author

R. H. Hardin Apr 24 2011

Status

approved