A080014 - OEIS

A080014

Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=2, I={1}.

1, 1, 1, 3, 6, 10, 18, 35, 65, 119, 221, 412, 764, 1416, 2629, 4881, 9057, 16807, 31194, 57894, 107442, 199399, 370065, 686799, 1274617, 2365544, 4390184, 8147680, 15121161, 28063153, 52082017, 96658283, 179386750, 332921362, 617864098

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

REFERENCES

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135

Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,-1,-1).

FORMULA

Recurrence: a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-4)-a(n-5)-a(n-6).

G.f.: -(x^2-1)/(x^6+x^5-x^4-x^3-x^2-x+1).

MATHEMATICA

LinearRecurrence[{1, 1, 1, 1, -1, -1}, {1, 1, 1, 3, 6, 10}, 40] (* Harvey P. Dale, Mar 10 2024 *)

PROG

(PARI) Vec(-(x^2-1)/(x^6+x^5-x^4-x^3-x^2-x+1)+O(x^99)) \\ Charles R Greathouse IV, Jun 12 2015

CROSSREFS