A080000 - OEIS

A080000

Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=3, I={-1,1,2}.

1, 1, 1, 1, 1, 2, 3, 5, 7, 9, 12, 16, 24, 35, 50, 70, 96, 135, 190, 270, 383, 539, 759, 1065, 1500, 2116, 2985, 4212, 5932, 8356, 11770, 16585, 23381, 32953, 46445, 65445, 92216, 129951, 183129, 258091, 363719, 512566, 722316, 1017886, 1434445, 2021476

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

OFFSET

0,6

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

Table of n, a(n) for n=0..45.

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

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 2, -1, 1, 0, 0, -1).

FORMULA

G.f.: -(x^5-1)/(x^10-x^7+x^6-2*x^5-x+1).

a(n) = a(n-1)+2*a(n-5)-a(n-6)+a(n-7)-a(n-10).

EXAMPLE

G.f. = 1 + x + x^2 + x^3 + x^4 + 2*x^5 + 3*x^6 + 5*x^7 + 7*x^8 + 9*x^9 + ...

a(5) = 2 for permutations [1,2,3,4,5] and [4,5,1,2,3].

CROSSREFS

Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.