A318496 Scaled g.f. T(v) = Sum_{n>=0} a(n)*(v/16)^n satisfies 15*(189*v-80)*T + d/dv(4*v*(27*v-5)*(27*v-32)*T') = 0, and a(0)=1; sequence gives a(n).

1, 30, 1440, 85260, 5606100, 391231080, 28360117800, 2110794125400, 160187289344100, 12339496371120600, 961855480344860640, 75700880007230883600, 6005580964527420946800, 479651805879329497831200, 38529018420812424368031600, 3110295017383730347887664560

Offset

0,2

Comments

Period function T(v) measures precession of the J-vector along an algebraic sphere curve with local cyclic C_3 symmetry. For precise definitions, pictures, a proof certificate, and more information, see A318495.

Links

Table of n, a(n) for n=0..15.

É. Goursat, Étude des surfaces qui admettent tous les plans de symétrie d'un polyèdre régulier, Annales scientifiques de l'École Normale Supérieure, Série 3 : Volume 4 (1887), 166-170.

Formula

10*n^2*a(n) - 3*(333*n^2-333*n+100)*a(n-1) + 324*(6*n-7)*(6*n-5)*a(n-2) = 0.

For n > 0, a(n) mod 30 = 0 (conjecture, tested up to n=10^6).

Mathematica

RecurrenceTable[{10 n^2 a[n] - 3 (333 n^2 - 333 n + 100) a[n-1] + 324 (6*n - 7) (6 n - 5) a[n-2] == 0, a[0] == 1, a[1] == 30}, a, {n, 0, 15}]

Prog

(GAP) a:=[1, 30];; for n in [3..20] do a[n]:=(1/(10*(n-1)^2))*(3*(333*(n^2-3*n+2)+100)*a[n-1]-(324*(6*n-13)*(6*n-11)*a[n-2])); od; a; # Muniru A Asiru, Sep 24 2018

Crossrefs

Cf. A318495. Periods: A186375, A318245, A318417.

Sequence in context: A353104 A048536 A369143 * A000173 A055351 A103917

Adjacent sequences: A318493 A318494 A318495 * A318497 A318498 A318499

Keyword

nonn

Author

Bradley Klee, Aug 27 2018

Status

approved