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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 February 19 15:01 EST 2018. Contains 299334 sequences. (Running on oeis4.)