A079987 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={-1,0,2}.

1, 0, 0, 1, 2, 3, 5, 7, 15, 29, 49, 84, 149, 268, 484, 855, 1508, 2684, 4784, 8516, 15134, 26873, 47782, 85004, 151149, 268704, 477685, 849299, 1510163, 2685089, 4773851, 8487625, 15090786, 26831239, 47705352, 84818268, 150803857, 268125092

Offset: 0

Author

Vladimir Baltic, Feb 17 2003

Keywords

• nonn

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={-2,0,1}.

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

• 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 (2, -2, 3, -2, 4, -1, -2, 4, -5, 4, -6, 3, 0, -2, 1, -2, 2, -1).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{2,-2,3,-2,4,-1,-2,4,-5,4,-6,3,0,-2,1,-2,2,-1},{1,0,0,1,2,3,5,7, 15,29, 49,84,149,268,484,855,1508,2684},40] (* Harvey P. Dale, Apr 29 2011 *)

Formula

a(n) = 2*a(n-1) -2*a(n-2) +3*a(n-3) -2*a(n-4) +4*a(n-5) -a(n-6) -2*a(n-7) +4*a(n-8) -5*a(n-9) +4*a(n-10) -6*a(n-11) +3*a(n-12) -2*a(n-14) +a(n-15) -2*a(n-16) +2*a(n-17) -a(n-18).

G.f.: -(x^12-2*x^11 +2*x^10-2*x^9 +2*x^8-x^7 -x^6+3*x^5 -2*x^4+2*x^3 -2*x^2+2*x -1)/( x^18 -2*x^17 +2*x^16 -x^15 +2*x^14 -3*x^12 +6*x^11 -4*x^10 +5*x^9 -4*x^8 +2*x^7 +x^6 -4*x^5 +2*x^4 -3*x^3 +2*x^2 -2*x+1)