A079994 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={0,1}.

1, 0, 0, 1, 3, 9, 13, 25, 59, 147, 328, 690, 1478, 3285, 7357, 16249, 35561, 77974, 171891, 379401, 835954, 1839288, 4047688, 8914186, 19636159, 43244340, 95216488, 209653186, 461673635, 1016681969, 2238835524, 4929989552

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={-1,0}.

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

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

Crossrefs

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

Sequence in context: A125706 A113510 A163795 * A303964 A124825 A074938

Adjacent sequences: A079991 A079992 A079993 * A079995 A079996 A079997

Keyword

nonn

Author

Vladimir Baltic, Feb 17 2003

Status

approved