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A079955 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={0,2,3}.

%I A079955 #35 Sep 08 2022 08:45:08
%S A079955 1,0,1,0,1,1,2,2,3,3,5,6,9,11,15,19,26,34,46,60,80,105,140,185,246,
%T A079955 325,431,570,756,1001,1327,1757,2328,3083,4085,5411,7169,9496,12580,
%U A079955 16664,22076,29244,38741,51320,67985,90060,119305,158045,209366,277350,367411
%N A079955 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={0,2,3}.
%C A079955 Number of compositions (ordered partitions) of n into elements of the set {2,5,6}.
%D A079955 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 A079955 G. C. Greubel, <a href="/A079955/b079955.txt">Table of n, a(n) for n = 0..1000</a>
%H A079955 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 A079955 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,1,1).
%F A079955 a(n) = a(n-2) + a(n-5) + a(n-6).
%F A079955 G.f.: 1/(1 - x^2 - x^5 - x^6).
%p A079955 seq(coeff(series(1/(1-x^2-x^5-x^6), x, n+1), x, n), n = 0..50); # _G. C. Greubel_, Dec 11 2019
%t A079955 LinearRecurrence[{0, 1, 0, 0, 1, 1}, {1, 0, 1, 0, 1, 1}, 51] (* _Jean-François Alcover_, Dec 11 2019 *)
%o A079955 (PARI) a(n) = ([0,1,0,0,0,0; 0,0,1,0,0,0; 0,0,0,1,0,0; 0,0,0,0,1,0; 0,0,0,0,0,1; 1,1,0,0,1,0]^n*[1;0;1;0;1;1])[1,1] \\ _Charles R Greathouse IV_, Jul 28 2015
%o A079955 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x^2-x^5-x^6) )); // _G. C. Greubel_, Dec 11 2019
%o A079955 (Sage)
%o A079955 def A079955_list(prec):
%o A079955     P.<x> = PowerSeriesRing(ZZ, prec)
%o A079955     return P( 1/(1-x^2-x^5-x^6) ).list()
%o A079955 A079955_list(50) # _G. C. Greubel_, Dec 11 2019
%Y A079955 Cf. A002524, A002525, A002526, A002527, A002528, A002529, A072827.
%Y A079955 Cf. A072850, A072851, A072852, A072853, A072854, A072855, A072856.
%Y A079955 Cf. A079955 - A080014.
%K A079955 nonn,easy
%O A079955 0,7
%A A079955 _Vladimir Baltic_, Feb 19 2003