A189591 Number of permutations of 1..n with displacements restricted to {-5,-4,-1,0,2,3}

1, 1, 2, 4, 10, 35, 107, 257, 585, 1423, 3505, 8633, 21808, 55437, 138452, 342488, 850499, 2117997, 5272078, 13136438, 32770428, 81689634, 203427274, 506595905, 1261968342, 3143705888, 7831363780, 19510741790, 48608257139, 121091284415

Offset

1,3

Links

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

Formula

Empirical: a(n) = a(n-1) +3*a(n-3) +7*a(n-4) +5*a(n-5) +17*a(n-6) +42*a(n-7) +55*a(n-8) -3*a(n-9) +14*a(n-10) -98*a(n-11) -183*a(n-12) -60*a(n-13) -175*a(n-14) -230*a(n-15) -280*a(n-16) -82*a(n-17) +5*a(n-18) +444*a(n-19) +903*a(n-20) -162*a(n-21) +332*a(n-22) +282*a(n-23) +638*a(n-24) +49*a(n-25) -39*a(n-26) -738*a(n-27) -1128*a(n-28) +308*a(n-29) -108*a(n-30) +75*a(n-31) -621*a(n-32) +310*a(n-33) -379*a(n-34) +403*a(n-35) +300*a(n-36) +14*a(n-37) +54*a(n-38) -13*a(n-39) +208*a(n-40) -131*a(n-41) +112*a(n-42) -65*a(n-43) -44*a(n-44) -22*a(n-45) +11*a(n-46) -8*a(n-47) -28*a(n-48) +11*a(n-49) -7*a(n-50) +3*a(n-51) +4*a(n-52) +2*a(n-53) -a(n-54) +a(n-56)

Example

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

Crossrefs

Sequence in context: A109455 A258948 A343158 * A189598 A156800 A210772

Adjacent sequences: A189588 A189589 A189590 * A189592 A189593 A189594

Keyword

nonn

Author

R. H. Hardin Apr 24 2011

Status

approved