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={-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
Stefano Spezia, Table of n, a(n) for n = 0..3000
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 (1,1,2,1,3,4,-7,-7,-6,6,-2,-1,1,4,1,-3,0,1,-1,-1).
FORMULA
a(n) = a(n-1) +a(n-2) +2*a(n-3) +a(n-4) +3*a(n-5) +4*a(n-6) -7*a(n-7) -7*a(n-8) -6*a(n-9) +6*a(n-10) -2*a(n-11) -a(n-12) +a(n-13) +4*a(n-14) +a(n-15) -3*a(n-16) +a(n-18) -a(n-19) -a(n-20).
G.f.: -(x^14 -x^12 +x^11 -x^9 -x^8 +x^6 -x^5 +3*x^3 +x^2-1)/( x^20 +x^19 -x^18 +3*x^16 -x^15 -4*x^14 -x^13 +x^12 +2*x^11 -6*x^10 +6*x^9 +7*x^8 +7*x^7 -4*x^6 -3*x^5 -x^4 -2*x^3 -x^2 -x +1).
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Baltic, Feb 17 2003
STATUS
approved