A286522 Floor of the volume of the d-th Chern-Vaaler star body.

2, 4, 8, 14, 23, 36, 52, 72, 93, 116, 138, 158, 174, 185, 191, 191, 186, 176, 162, 146, 128, 110, 93, 77, 62, 49, 38, 29, 22, 16, 12, 8, 6, 4, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,1

Comments

Unimodal: increases from 2 to a maximum of 191, then decreases to 0 = a(d) for d >= 38 (see Grizzard and Gunther, 2016, Lemma 2.2). See A286523 for other comments, references, links, formulas, and programs. For the "monic slice" of the star body, see A288756, A288757, A288758.

Links

Table of n, a(n) for n=0..73.

Robert Grizzard and Joseph Gunther, Slicing the stars: counting algebraic numbers, integers, and units by degree and height, arXiv:1609.08720 [math.NT] 2016.

Formula

a(n) = floor(A286523(n) / A286524(n)).

Mathematica

a[d_] := (e = Floor[(d-1)/2]; 2^(d+1) (d+1)^e Product[(2k)^(d-2k)/(2k+1)^( d+1-2k), {k, 1, e}]) // Floor;
Table[a[d], {d, 0, 39}] (* Jean-François Alcover, Dec 04 2018, after Jonathan Sondow in A286523 *)

Prog

(PARI) a(n) = floor(2^(n+1)*(n+1)^((n-1)\2)*prod(k=1, (n-1)\2, (2*k)^(n-2*k)/(2*k+1)^(n+1-2*k))); \\ Jinyuan Wang, Mar 05 2020

Crossrefs

Cf. A286523, A286524, A288756, A288757, A288758.

Sequence in context: A261968 A138526 A389737 * A201347 A089054 A055291

Adjacent sequences: A286519 A286520 A286521 * A286523 A286524 A286525

Keyword

nonn

Author

Jonathan Sondow, May 26 2017

Extensions

More terms from Jinyuan Wang, Mar 05 2020

Status

approved