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%I M4399 #44 Jan 28 2022 07:44:29
%S 1,7,31,115,391,1267,3979,12271,37423,113371,342091,1029799,3095671,
%T 9298147,27914179,83777503,251394415,754292827,2263072411,6789560407,
%U 20369288455,61108939795,183328720435,549989524879,1649974525855,4949934107083,14849820951115
%N Number of elements in Z[ omega ] whose 'smallest algorithm' is <= n, where omega^2 = -omega - 1.
%C omega is a primitive third root of unity. - _Joerg Arndt_, Apr 29 2021
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A006458/b006458.txt">Table of n, a(n) for n = 0..1000</a>
%H H. W. Lenstra, Jr., <a href="/A006457/a006457.pdf">Letter to N. J. A. Sloane, Nov. 1975</a>
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.
%H P. Samuel, <a href="https://doi.org/10.1016/0021-8693(71)90110-4">About Euclidean rings</a>, J. Alg., 19 (1971), 282-301.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,-5,-5,4,8,-6).
%F a(n+6) - 5*a(n+5) + 5*a(n+4) + 5*a(n+3) - 4*a(n+2) - 8*a(n+1) + 6*a(n) = 0.
%F G.f.: (x*(6*x^4+2*x^3+x+2)+1)/((x-1)^2*(3*x-1)*(2*x^2*(x+1)-1)). - _Harvey P. Dale_, Mar 03 2012
%p A006458:=(1+2*z+z**2+2*z**4+6*z**5)/(3*z-1)/(2*z**3+2*z**2-1)/(z-1)**2; # Conjectured by _Simon Plouffe_ in his 1992 dissertation
%t LinearRecurrence[{5,-5,-5,4,8,-6},{1,7,31,115,391,1267},40] (* _Harvey P. Dale_, Mar 03 2012 *)
%Y Cf. A006457, A006459.
%K nonn,easy,nice
%O 0,2
%A H. W. Lenstra, Jr.
%E Corrected by _T. D. Noe_, Nov 08 2006
%E More terms from _Harvey P. Dale_, Mar 03 2012
%E Name corrected by _Joerg Arndt_, Apr 29 2021
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