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A239487 Maximum number of diameters of an indecomposable algebraic curve of degree n. 0
3, 6, 5, 12, 7, 18, 9, 12, 11, 30, 13, 16, 15, 18, 17, 20, 19, 30, 21, 24, 23, 30, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 48, 47, 50, 49, 52, 51, 54, 53, 56, 55, 58, 57, 60, 59, 62, 61, 64, 63, 66, 65, 68, 67, 70 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

REFERENCES

F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, p. 70, 1983 (apparently there is an error concerning the list of exceptions: Le Lionnais has 10, 12, 24, whereas both Lebesgue papers say 12, 20, 24).

LINKS

Table of n, a(n) for n=3..68.

Henri Lebesgue, Sur les diamètres rectilignes des courbes algébriques planes, Bulletin de la Société Mathématique de France, 49 (1921), pp. 109-150.

Henri Lebesgue, Les Coniques, Préface de M. Paul Montel, Paris, Gauthier-Villars, 1942

FORMULA

a(n) = n if n is odd, a(n) = n + 2 if n is even except for a(6) = 12, a(8) = 18, a(12) = a(20) = a(24) = 30, and a(16) = 18.

Empirical g.f.: x^3*(4*x^24 -4*x^23 -4*x^22 +4*x^21 +8*x^20 -8*x^19 -8*x^18 +8*x^17 +16*x^12 -16*x^11 -16*x^10 +16*x^9 +8*x^8 -8*x^7 -4*x^6 +4*x^5 -4*x^4 +4*x^3 -4*x^2 +3*x +3) / ((x -1)^2*(x +1)). - Colin Barker, Sep 23 2014

PROG

(PARI) a(n) = if (n % 2, n, if (n == 6, 12, if (n == 8, 18, if ((n==12) ||(n==20) ||(n==24) , 30, if (n==16, 18, n+2)))));

CROSSREFS

Sequence in context: A007479 A076535 A285327 * A246979 A246980 A095359

Adjacent sequences:  A239484 A239485 A239486 * A239488 A239489 A239490

KEYWORD

nonn

AUTHOR

Michel Marcus, Mar 20 2014

STATUS

approved

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Last modified August 10 12:19 EDT 2020. Contains 336379 sequences. (Running on oeis4.)