A239487 Maximum number of diameters of an indecomposable algebraic curve of degree n.

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

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: A076535 A349102 A285327 * A246979 A246980 A095359

Adjacent sequences: A239484 A239485 A239486 * A239488 A239489 A239490

Keyword

nonn

Author

Michel Marcus, Mar 20 2014

Status

approved