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A017818 Expansion of 1/(1-x^3-x^4-x^5).

%I A017818 #54 Mar 06 2025 10:54:40
%S A017818 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 A017818 392,520,689,912,1208,1601,2121,2809,3721,4930,6531,8651,11460,15182,
%U A017818 20112,26642,35293,46754,61936,82047
%N A017818 Expansion of 1/(1-x^3-x^4-x^5).
%C A017818 Compositions of n into parts 3, 4, and 5. - _David Neil McGrath_, Jul 28 2014
%C A017818 The number of ways a T2 triangle can cover a row length of T1(n) triangles. - _Craig Knecht_, Mar 06 2025
%H A017818 Vincenzo Librandi, <a href="/A017818/b017818.txt">Table of n, a(n) for n = 0..1000</a>
%H A017818 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 A017818 Craig Knecht, <a href="/A017818/a017818.png">The number of ways a T2 triangle can cover a row of T1 triangles</a>.
%H A017818 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1,1).
%F A017818 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 A017818 a(n) = a(n-5) + a(n-4) + a(n-3). - _Jon E. Schoenfield_, Aug 07 2006
%F A017818 a(2n+3) = A060945(n). - _Yasuyuki Kachi_, Jul 06 2024
%t A017818 CoefficientList[Series[1 / (1 - x^3 - x^4 - x^5), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 27 2013 *)
%t A017818 LinearRecurrence[{0,0,1,1,1},{1,0,0,1,1},50] (* _Harvey P. Dale_, Oct 03 2020 *)
%o A017818 (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x^3-x^4-x^5))); // _Vincenzo Librandi_, Jun 27 2013
%o A017818 (Magma) 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 A017818 nonn,easy
%O A017818 0,8
%A A017818 _N. J. A. Sloane_