%I #11 Jul 29 2024 10:03:19

%S 1,1,1,1,3,6,12,20,35,60,114,207,375,671,1213,2180,3954,7139,12892,

%T 23250,41996,75793,136891,247133,446211,805505,1454390,2625744,

%U 4740788,8559108,15453182,27899503,50371415,90942627,164192549,296440115

%N 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={-2,1,2}.

%C 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,-1,2}.

%D 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.

%H Vladimir Baltic, <a href="http://pefmath.etf.rs/vol4num1/AADM-Vol4-No1-119-135.pdf">On the number of certain types of strongly restricted permutations</a>, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (2010), 119-135

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 1, 0, -1, 4, -4, -3, -3, 3, 3, -5, 4, 4, 1, -2, -1, 1, -1, -1).

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

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

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

%K nonn,changed

%O 0,5

%A _Vladimir Baltic_, Feb 17 2003