A079985 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-1,0,1}.

1, 0, 0, 0, 1, 2, 4, 0, 4, 10, 29, 40, 64, 88, 221, 420, 800, 1280, 2336, 4260, 8325, 15000, 27200, 48360, 89541, 164430, 303300, 549120, 1001156, 1824342, 3350169, 6122640, 11189504, 20391280, 37266329, 68097480, 124548224, 227452928, 415474816

Offset: 0

Author

Vladimir Baltic, Feb 17 2003

Keywords

• nonn

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
• Index entries for linear recurrences with constant coefficients, signature (1, 1, -1, 3, 2, 2, -6, -2, 2, -3, -1, -1, 1, 1).

Crossrefs

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

Formula

a(n) = a(n-1) +a(n-2) -a(n-3) +3*a(n-4) +2*a(n-5) +2*a(n-6) -6*a(n-7) -2*a(n-8) +2*a(n-9) -3*a(n-10) -a(n-11) -a(n-12) +a(n-13) +a(n-14)

G.f.: -(x^8+x^7-x^6-x^5-2*x^4+x^3-x^2-x+1)/(x^14 +x^13 -x^12 -x^11 -3*x^10 +2*x^9 -2*x^8 -6*x^7 +2*x^6 +2*x^5 +3*x^4 -x^3 +x^2 +x-1)