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A222072 Decimal expansion of (1/384)*Pi^4. 12
2, 5, 3, 6, 6, 9, 5, 0, 7, 9, 0, 1, 0, 4, 8, 0, 1, 3, 6, 3, 6, 5, 6, 3, 3, 6, 6, 3, 7, 6, 8, 3, 6, 2, 2, 7, 2, 1, 2, 8, 3, 2, 2, 5, 4, 3, 5, 5, 9, 5, 1, 6, 1, 8, 9, 8, 8, 1, 9, 7, 5, 5, 0, 4, 9, 4, 7, 1, 5, 7, 6, 9, 4, 1, 8, 8, 2, 0, 8, 2, 3, 4, 1, 1, 7, 7, 5, 6, 9, 5, 9, 2, 3, 8, 3, 5, 9, 1, 8, 1, 0, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Conjectured to be density of densest packing of equal spheres in 8 dimensions (achieved for example by the D_8 lattice).

The above conjecture is true (cf. Viazovska, 2017). - Felix Fröhlich, Jan 08 2018

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. xix.

LINKS

Table of n, a(n) for n=0..101.

J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discrete & Computational Geometry, Vol. 13, No. 3-4 (1995), 383-403.

G. Nebe and N. J. A. Sloane, Home page for E_8 lattice

N. J. A. Sloane, Table of maximal density of a packing of equal spheres in n-dimensional Euclidean space (for n>3 the values are only conjectural).

M. S. Viazovska, The sphere packing problem in dimension 8, Annals of Mathematics, Vol. 185, No. 3 (2017), 991-1015.

M. S. Viazovska, The sphere packing problem in dimension 8, arXiv:1603.04246 [math.NT], 2017.

FORMULA

Equals Sum_{n>=1} Sum_{k>=n} 1/(2*n - 1)^2/(2*k + 1)^2. - Geoffrey Critzer, Nov 03 2013

EXAMPLE

.25366950790104801363656336637683622721283225435595161898819...

MATHEMATICA

RealDigits[Pi^4/ 384, 10, 120][[1]] (* Harvey P. Dale, Aug 11 2015 *)

PROG

(PARI) Pi^4/384 \\ Charles R Greathouse IV, Oct 31 2014

CROSSREFS

Related constants: A020769, A020789, A093766, A093825, A222066, A222067, A222068, A222069, A222070, A222071, A222073, A222074, A222075.

Sequence in context: A160516 A264105 A024871 * A246007 A256997 A239970

Adjacent sequences:  A222069 A222070 A222071 * A222073 A222074 A222075

KEYWORD

nonn,cons

AUTHOR

N. J. A. Sloane, Feb 10 2013

STATUS

approved

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Last modified October 16 12:00 EDT 2019. Contains 328056 sequences. (Running on oeis4.)