A239077 Number of self-inverse permutations p on [n] with displacement of elements restricted by 5: |p(i)-i| <= 5.

1, 1, 2, 4, 10, 26, 76, 206, 546, 1406, 3608, 9259, 23981, 62324, 162224, 422028, 1096900, 2848240, 7394076, 19196044, 49844356, 129443736, 336182997, 873106045, 2267493182, 5888625652, 15292437454, 39713590230, 103134439084, 267836774530, 695564961926

Offset

0,3

Comments

Column k=5 of A238888.

Links

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

Formula

G.f.: -(x^22 +2*x^17 -10*x^12 -2*x^11 +2*x^10 -2*x^9 -2*x^8 +6*x^7 +4*x^6 -2*x^5 +2*x^4 +2*x^3 +2*x^2-1) / (x^32 +x^31 +x^30 -x^29 -x^28 +7*x^27 +5*x^26 +x^25 -5*x^24 -3*x^23 -x^22 -8*x^21 -16*x^20 +8*x^18 -40*x^17 -36*x^16 +20*x^14 +12*x^13 +64*x^12 +52*x^11 +19*x^10 -5*x^9 -13*x^8 -27*x^7 -19*x^6 +x^5 -x^4 -x^3 -3*x^2 -x+1).

Maple

gf:= -(x^22 +2*x^17 -10*x^12 -2*x^11 +2*x^10 -2*x^9 -2*x^8 +6*x^7 +4*x^6 -2*x^5 +2*x^4 +2*x^3 +2*x^2-1) / (x^32 +x^31 +x^30 -x^29 -x^28 +7*x^27 +5*x^26 +x^25 -5*x^24 -3*x^23 -x^22 -8*x^21 -16*x^20 +8*x^18 -40*x^17 -36*x^16 +20*x^14 +12*x^13 +64*x^12 +52*x^11 +19*x^10 -5*x^9 -13*x^8 -27*x^7 -19*x^6 +x^5 -x^4 -x^3 -3*x^2 -x+1):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);

Mathematica

CoefficientList[Series[-(x^22 + 2 x^17 - 10 x^12 - 2 x^11 + 2 x^10 - 2 x^9 - 2 x^8 + 6 x^7 + 4 x^6 - 2 x^5 + 2 x^4 + 2 x^3 + 2 x^2 - 1)/(x^32 + x^31 + x^30 - x^29 - x^28 + 7 x^27 + 5 x^26 + x^25 - 5 x^24 - 3 x^23 - x^22 - 8 x^21 - 16 x^20 + 8 x^18 - 40 x^17 - 36 x^16 + 20 x^14 + 12 x^13 + 64 x^12 + 52 x^11 + 19 x^10 - 5 x^9 - 13 x^8 - 27 x^7 - 19 x^6 + x^5 - x^4 - x^3 - 3 x^2 - x + 1), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 12 2014 *)

Crossrefs

Cf. A000085, A238888.

Sequence in context: A006251 A049401 A294672 * A148099 A007579 A239078

Adjacent sequences: A239074 A239075 A239076 * A239078 A239079 A239080

Keyword

nonn,easy

Author

Joerg Arndt and Alois P. Heinz, Mar 10 2014

Status

approved