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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).

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

REFERENCES

J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discr. Comp. Geom., 13 (1995), 383-403.

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.

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).

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 March 27 02:45 EDT 2017. Contains 284144 sequences.