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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}. 77
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
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135
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
Sequence in context: A261631 A029864 A075111 * A364403 A360892 A132274
KEYWORD
nonn,easy
AUTHOR
Vladimir Baltic, Jan 24 2003
STATUS
approved

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Last modified April 25 04:42 EDT 2024. Contains 371964 sequences. (Running on oeis4.)