login
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
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
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
KEYWORD
nonn
AUTHOR
Michel Marcus, Mar 20 2014
STATUS
approved