A079997 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, 0, 1, 2, 9, 24, 57, 140, 376, 1016, 2692, 7020, 18369, 48344, 127465, 335510, 882081, 2319136, 6100393, 16049440, 42220168, 111053856, 292109320, 768373144, 2021186393, 5316647448, 13985104873, 36786882378, 96765680857, 254536684328

Offset

0,4

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

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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 (1, 3, 0, 6, 10, 0, -12, -10, -2, 0, 0, -1, 1, 1).

Formula

a(n) = a(n-1)+3*a(n-2)+6*a(n-4)+10*a(n-5)-12*a(n-7)-10*a(n-8)-2*a(n-9)-a(n-12)+a(n-13)+a(n-14)

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

Mathematica

LinearRecurrence[{1, 3, 0, 6, 10, 0, -12, -10, -2, 0, 0, -1, 1, 1}, {1, 0, 1, 2, 9, 24, 57, 140, 376, 1016, 2692, 7020, 18369, 48344}, 40] (* Harvey P. Dale, Nov 27 2013 *)

Crossrefs

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

Column k=3 of A259776.

Cf. A260081.

Sequence in context: A131357 A274543 A356114 * A351252 A275260 A248436

Adjacent sequences: A079994 A079995 A079996 * A079998 A079999 A080000

Keyword

nonn,easy

Author

Vladimir Baltic, Feb 17 2003

Status

approved