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%I #37 Feb 26 2024 11:00:52
%S 1,0,0,1,1,1,1,2,3,3,4,6,8,10,13,18,24,31,41,55,73,96,127,169,224,296,
%T 392,520,689,912,1208,1601,2121,2809,3721,4930,6531,8651,11460,15182,
%U 20112,26642,35293,46754,61936,82047
%N Expansion of 1/(1-x^3-x^4-x^5).
%C Compositions of n into parts 3, 4, and 5. - _David Neil McGrath_, Jul 28 2014
%H Vincenzo Librandi, <a href="/A017818/b017818.txt">Table of n, a(n) for n = 0..1000</a>
%H Tomislav Došlić, Mate Puljiz, Stjepan Šebek, and Josip Žubrinić, <a href="https://arxiv.org/abs/2401.01225">Predators and altruists arriving on jammed Riviera</a>, arXiv:2401.01225 [math.CO], 2024. See p. 14.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1,1).
%F a(n) = (1/10)*(2*A001608(n) + 2*A000931(n+2) + (-1)^floor(n/2) - 3(-1)^floor((n-1)/2)). - _Ralf Stephan_, Jun 09 2005
%F a(n) = a(n-5) + a(n-4) + a(n-3). - _Jon E. Schoenfield_, Aug 07 2006
%t CoefficientList[Series[1 / (1 - x^3 - x^4 - x^5), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)
%t LinearRecurrence[{0,0,1,1,1},{1,0,0,1,1},50] (* _Harvey P. Dale_, Oct 03 2020 *)
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^3-x^4-x^5))); /* or */ I:=[1,0,0,1,1]; [n le 5 select I[n] else Self(n-3)+Self(n-4)+Self(n-5): n in [1..50]]; // _Vincenzo Librandi_, Jun 27 2013
%K nonn,easy
%O 0,8
%A _N. J. A. Sloane_.
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