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 A006458 Number of elements in Z[ omega ] whose `smallest algorithm' is <= n, where omega = -omega+1. (Formerly M4399) 3
 1, 7, 31, 115, 391, 1267, 3979, 12271, 37423, 113371, 342091, 1029799, 3095671, 9298147, 27914179, 83777503, 251394415, 754292827, 2263072411, 6789560407, 20369288455, 61108939795, 183328720435, 549989524879, 1649974525855, 4949934107083, 14849820951115 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES P. Samuel, About Euclidean rings, J. Alg., 19 (1971), 282-301. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 H. W. Lenstra, Jr., Letter to N. J. A. Sloane, Nov. 1975 Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. Index entries for linear recurrences with constant coefficients, signature (5, -5, -5, 4, 8, -6). FORMULA a(n+6)-5a(n+5)+5a(n+4)+5a(n+3)-4a(n+2)-8a(n+1)+6a(n)=0. G.f.: (x*(6*x^4+2*x^3+x+2)+1)/((x-1)^2*(3*x-1)*(2*x^2*(x+1)-1)) [From Harvey P. Dale, Mar 03 2012] MAPLE 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.] MATHEMATICA LinearRecurrence[{5, -5, -5, 4, 8, -6}, {1, 7, 31, 115, 391, 1267}, 40] (* Harvey P. Dale, Mar 03 2012 *) CROSSREFS Cf. A006457, A006459. Sequence in context: A055580 A097786 A197649 * A091344 A032197 A114289 Adjacent sequences:  A006455 A006456 A006457 * A006459 A006460 A006461 KEYWORD nonn,easy,nice AUTHOR H. W. Lenstra, Jr. EXTENSIONS Corrected by T. D. Noe, Nov 08 2006 More terms from Harvey P. Dale, Mar 03 2012 STATUS approved

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)