A239075 Number of self-inverse permutations p on [n] with displacement of elements restricted by 3: |p(i)-i| <= 3.

1, 1, 2, 4, 10, 22, 48, 103, 225, 492, 1076, 2348, 5124, 11184, 24417, 53305, 116366, 254024, 554534, 1210554, 2642656, 5768943, 12593649, 27492040, 60015368, 131014088, 286004920, 624351264, 1362964321, 2975363169, 6495244138, 14179175436, 30953265426

Offset

0,3

Comments

Column k=3 of A238888.

Also the number of compositions of n into m sorts of k's, where m=1 if k=1,2,3, m=2 if k>6 and m=3 if k=4,5,6. - Beimar Naranjo, Mar 05 2024

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: -(x-1)/(x^7-2*x^4-2*x+1).

Maple

gf:= -(x-1)/(x^7-2*x^4-2*x+1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[(1 - x)/(x^7 - 2 x^4 - 2 x + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 12 2014 *)

Crossrefs

Cf. A000085, A238888.

Sequence in context: A018108 A033497 A327471 * A260916 A192627 A275445

Adjacent sequences: A239072 A239073 A239074 * A239076 A239077 A239078

Keyword

nonn,easy

Author

Joerg Arndt and Alois P. Heinz, Mar 10 2014

Status

approved