login
Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=5, I={0,1,4}.
2

%I #16 Apr 16 2024 10:28:50

%S 1,0,0,1,1,0,2,2,1,3,5,3,6,10,9,12,21,22,27,43,52,61,91,117,140,195,

%T 260,318,426,572,718,939,1258,1608,2083,2769,3584,4630,6110,7961,

%U 10297,13509,17655,22888,29916,39125,50840,66313,86696,112853,147069,192134

%N Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=5, I={0,1,4}.

%C Number of compositions (ordered partitions) of n into elements of the set {3,4,6}.

%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_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1,0,1).

%F a(n) = a(n-3)+a(n-4)+a(n-6).

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

%t LinearRecurrence[{0,0,1,1,0,1},{1,0,0,1,1,0},60] (* _Harvey P. Dale_, Oct 05 2016 *)

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

%K nonn,easy

%O 0,7

%A _Vladimir Baltic_, Feb 19 2003