A079989 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={1,2}.

1, 1, 1, 1, 5, 13, 27, 51, 103, 221, 498, 1064, 2240, 4728, 10076, 21559, 46075, 98085, 208759, 444727, 948151, 2021335, 4307861, 9179111, 19560273, 41686260, 88842852, 189337896, 403497908, 859893060, 1832537757, 3905386173, 8322891733, 17737112293, 37799944529

Offset: 0

Author

Vladimir Baltic, Feb 17 2003

Keywords

• nonn
• easy

Comments

Also, 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={-2,-1}.

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

• Stefano Spezia, Table of n, a(n) for n = 0..3000
• 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 (1,1,2,1,3,4,-7,-7,-6,6,-2,-1,1,4,1,-3,0,1,-1,-1).

Crossrefs

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

Formula

a(n) = a(n-1) +a(n-2) +2*a(n-3) +a(n-4) +3*a(n-5) +4*a(n-6) -7*a(n-7) -7*a(n-8) -6*a(n-9) +6*a(n-10) -2*a(n-11) -a(n-12) +a(n-13) +4*a(n-14) +a(n-15) -3*a(n-16) +a(n-18) -a(n-19) -a(n-20).

G.f.: -(x^14 -x^12 +x^11 -x^9 -x^8 +x^6 -x^5 +3*x^3 +x^2-1)/( x^20 +x^19 -x^18 +3*x^16 -x^15 -4*x^14 -x^13 +x^12 +2*x^11 -6*x^10 +6*x^9 +7*x^8 +7*x^7 -4*x^6 -3*x^5 -x^4 -2*x^3 -x^2 -x +1).