A079969 - OEIS

%I #19 Apr 16 2024 04:17:37

%S 1,1,2,3,6,11,21,38,70,128,236,434,799,1469,2702,4969,9140,16811,

%T 30921,56872,104604,192396,353872,650872,1197141,2201885,4049898,

%U 7448923,13700706,25199527,46349157,85249390,156798074,288396620,530444084

%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={2}.

%C Number of compositions (ordered partitions) of n into elements of the set {1,2,4,5,6}.

%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 (1,1,0,1,1,1).

%F a(n) = a(n-1)+a(n-2)+a(n-4)+a(n-5)+a(n-6).

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

%t LinearRecurrence[{1,1,0,1,1,1},{1,1,2,3,6,11},40] (* _Harvey P. Dale_, Aug 03 2014 *)

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

%K nonn,easy

%O 0,3

%A _Vladimir Baltic_, Feb 19 2003