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={-2,1}.
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
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, 1, 2, 1, 4, 7, -4, -1, 1, 7, 3, -7, 2, 3, 0, -3, -2, 1, -1, -1).
FORMULA
a(n) = a(n-1) +a(n-2) +2*a(n-3) +a(n-4) +4*a(n-5) +7*a(n-6) -4*a(n-7) -a(n-8) +a(n-9) +7*a(n-10) +3*a(n-11) -7*a(n-12) +2*a(n-13) +3*a(n-14) -3*a(n-16) -2*a(n-17) +a(n-18) -a(n-19) -a(n-20).
G.f.: -(x^14-x^12+2*x^11-x^9+2*x^6-x^5+2*x^3+x^2-1)/(x^20 +x^19 -x^18 +2*x^17 +3*x^16 -3*x^14 -2*x^13 +7*x^12 -3*x^11 -7*x^10 -x^9 +x^8 +4*x^7 -7*x^6 -4*x^5 -x^4 -2*x^3 -x^2 -x+1)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Baltic, Feb 17 2003
STATUS
approved