login
Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=3, I={-1,0}.
1

%I #15 Apr 16 2024 03:22:01

%S 1,0,0,1,2,2,3,5,11,15,24,40,68,110,177,290,480,783,1278,2090,3427,

%T 5609,9171,15005,24564,40200,65776,107628,176137,288244,471676,771845,

%U 1263074,2066938,3382367,5534941,9057495,14821891,24254820,39691008

%N Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=2, r=3, I={-1,0}.

%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_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,2,2,0,-1,0,-1,-1).

%F Recurrence: a(n) = a(n-2)+a(n-3)+2*a(n-4)+2*a(n-5)-a(n-7)-a(n-9)-a(n-10).

%F G.f.: -(x^5+x^2-1)/((x^9+x^6-x^5-x^4-x^3-x+1)*(x+1))

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

%K nonn

%O 0,5

%A _Vladimir Baltic_, Feb 10 2003