%I #21 Apr 16 2024 04:14:48

%S 1,1,1,2,4,6,10,17,28,46,77,128,212,352,585,971,1612,2677,4445,7380,

%T 12254,20347,33784,56095,93141,154652,256785,426368,707945,1175477,

%U 1951771,3240736,5380943,8934559,14835011,24632167,40899440,67909746

%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={1,4}.

%C Number of compositions (ordered partitions) of n into elements of the set {1,3,4,6}.

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

%F a(n) = a(n-1)+a(n-3)+a(n-4)+a(n-6).

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

%p g:=1/(1-z-z^3-z^4-z^6): gser:=series(g, z=0, 49): seq((coeff(gser, z, n)), n=0..37); # _Zerinvary Lajos_, Apr 17 2009

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

%K nonn,easy

%O 0,4

%A _Vladimir Baltic_, Feb 19 2003