A079982 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={-1,0,1,2}.

1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 4, 1, 1, 1, 1, 10, 10, 7, 7, 11, 20, 50, 40, 49, 61, 85, 175, 225, 265, 323, 461, 665, 1085, 1310, 1728, 2290, 3171, 4767, 6489, 8618, 11374, 15751, 21813, 31263, 41749, 56596, 76735, 105514, 147726, 202628, 276079, 374275

Offset

0,12

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,-1,0,1}.

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

Table of n, a(n) for n=0..52.

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

Formula

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

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

Mathematica

LinearRecurrence[{0, 1, 0, 0, 2, 3, -1, -3, 1, -1, -1, -3, 1, 3, -2, 0, 0, 1, 0, -1}, {1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 4, 1, 1, 1, 1, 10, 10, 7, 7}, 60] (* Harvey P. Dale, Dec 19 2021 *)

Crossrefs

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

Sequence in context: A350388 A056623 A038025 * A265143 A181873 A229293

Adjacent sequences: A079979 A079980 A079981 * A079983 A079984 A079985

Keyword

nonn,easy,changed

Author

Vladimir Baltic, Feb 17 2003

Status

approved