A079986 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={-2,0,2}.

1, 0, 1, 0, 4, 0, 16, 0, 49, 0, 169, 0, 576, 0, 1936, 0, 6561, 0, 22201, 0, 75076, 0, 254016, 0, 859329, 0, 2907025, 0, 9834496, 0, 33269824, 0, 112550881, 0, 380757169, 0, 1288092100, 0, 4357584144, 0, 14741602225

Offset: 0

Author

Vladimir Baltic, Feb 17 2003

Keywords

• nonn

Comments

a(n)=( A000073(k+2) )^2 if n=2k, a(n)=0 otherwise.

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 (0, 2, 0, 3, 0, 6, 0, -1, 0, 0, 0, -1).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{0,2,0,3,0,6,0,-1,0,0,0,-1},{1,0,1,0,4,0,16,0,49,0,169,0},50] (* Harvey P. Dale, Nov 03 2015 *)

Formula

a(n) = 2*a(n-2)+3*a(n-4)+6*a(n-6)-a(n-8)-a(n-12).

G.f.: -(x^6+x^4+x^2-1)/(x^12+x^8-6*x^6-3*x^4-2*x^2+1)