A079993 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={0,2}.

1, 0, 1, 1, 5, 9, 23, 39, 97, 197, 465, 969, 2161, 4605, 10202, 22051, 48438, 105028, 229692, 499620, 1091268, 2376641, 5185742, 11299467, 24645179, 53718931, 117144203, 255371099, 556824105, 1213941393, 2646824821, 5770590379

Offset

0,5

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}.

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..31.

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

Formula

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

G.f.: -(x^3+1)*(x^11-x^9-2*x^8-x^7+2*x^6+x^4+2*x^3+x^2-1)/((x^18 -x^17 -2*x^16 +3*x^15 +x^14 -4*x^13 -4*x^12 +7*x^11 +7*x^10 -6*x^9 +3*x^8 +7*x^7 -4*x^6 -4*x^5 -3*x^4 +x^3 -2*x^2 -x+1) *(x^2+x+1)).

Crossrefs

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

Sequence in context: A229925 A280030 A074340 * A163607 A067294 A271543

Adjacent sequences: A079990 A079991 A079992 * A079994 A079995 A079996

Keyword

nonn

Author

Vladimir Baltic, Feb 17 2003

Status

approved