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%I A079816 #27 Dec 13 2023 08:32:10
%S A079816 1,1,1,2,4,7,12,20,34,59,102,175,300,515,885,1521,2613,4488,7709,
%T A079816 13243,22750,39081,67134,115324,198107,340315,584604,1004250,1725130,
%U A079816 2963480,5090756,8745055,15022519,25806135,44330556,76152366,130816831
%N A079816 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}.
%C A079816 Number of compositions (ordered partitions) of n into elements of the set {1,3,4,5,6}.
%C A079816 a(n+1) is the number of multus bitstrings of length n with no runs of 6 ones. - _Steven Finch_, Mar 25 2020
%D A079816 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 A079816 G. C. Greubel, <a href="/A079816/b079816.txt">Table of n, a(n) for n = 0..1000</a>
%H A079816 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 A079816 Steven Finch, <a href="https://arxiv.org/abs/2003.09458">Cantor-solus and Cantor-multus distributions</a>, arXiv:2003.09458 [math.CO], 2020.
%H A079816 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,1,1,1).
%F A079816 Recurrence: a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-6).
%F A079816 G.f.: 1/(1-x-x^3-x^4-x^5-x^6).
%t A079816 LinearRecurrence[{1,0,1,1,1,1}, {1,1,1,2,4,7}, 51] (* _G. C. Greubel_, Dec 12 2023 *)
%o A079816 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x-x^3-x^4-x^5-x^6) )); // _G. C. Greubel_, Dec 12 2023
%o A079816 (SageMath)
%o A079816 def A079816_list(prec):
%o A079816     P.<x> = PowerSeriesRing(ZZ, prec)
%o A079816     return P( 1/(1-x-x^3-x^4-x^5-x^6) ).list()
%o A079816 A079816_list(50) # _G. C. Greubel_, Dec 12 2023
%Y A079816 Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
%K A079816 nonn
%O A079816 0,4
%A A079816 _Vladimir Baltic_, Feb 19 2003

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