A079996 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}.

1, 1, 1, 3, 11, 33, 82, 198, 516, 1389, 3690, 9642, 25143, 65867, 173092, 454578, 1192227, 3125940, 8198836, 21509532, 56429115, 148023671, 388279519, 1018515853, 2671777153, 7008626377, 18384947908, 48227023198, 126508325008

Offset

0,4

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}.

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..28.

Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics 4 (2010), 119-135

Index entries for linear recurrences with constant coefficients, signature (1, 2, 3, 4, 9, 9, -15, -12, 0, 7, -6, -6, 5, 5, 3, -2, -1, 2, -1, -1).

Formula

a(n) = a(n-1) +2*a(n-2) +3*a(n-3) +4*a(n-4) +9*a(n-5) +9*a(n-6) -15*a(n-7) -12*a(n-8) +7*a(n-10) -6*a(n-11) -6*a(n-12) +5*a(n-13) +5*a(n-14) +3*a(n-15) -2*a(n-16) -a(n-17) +2*a(n-18) -a(n-19) -a(n-20).

G.f.: -(x^14 -2*x^12 +x^11 -x^10 -2*x^8 -2*x^7 +4*x^6 +x^4 +3*x^3 +2*x^2-1) /(x^20 +x^19 -2*x^18 +x^17 +2*x^16 -3*x^15 -5*x^14 -5*x^13 +6*x^12 +6*x^11 -7*x^10 +12*x^8 +15*x^7 -9*x^6 -9*x^5 -4*x^4 -3*x^3 -2*x^2 -x+1)

Crossrefs

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

Sequence in context: A034561 A131747 A295626 * A288038 A186308 A352102

Adjacent sequences: A079993 A079994 A079995 * A079997 A079998 A079999

Keyword

nonn

Author

Vladimir Baltic, Feb 17 2003

Status

approved