OFFSET
0,2
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, p. 151.
Robert L. Griess Jr., Pieces of 2^d: Existence and uniqueness for Barnes-Wall and Ypsilanti lattices, arXiv:math/0403480 [math.GR], Mar 28 2004. See Proposition 8.9.
J. Leech, Some sphere packings in higher space, Canad. J. Math., 16 (1964), 657-682.
J. Leech & N. J. A. Sloane, Correspondence, 1975
C. Musès, The dimensional family approach in (hyper)sphere packing..., Applied Math. Computation 88 (1997), pp. 1-26, see p. 22.
G. Nebe and N. J. A. Sloane, Table of highest kissing numbers known
FORMULA
a(n) = (2+2)(2+4)(2+8)(2+16)...(2+2^n).
From Paul D. Hanna, Sep 16 2009: (Start)
G.f.: Sum_{n>=0} 2^(n*(n+1)/2) * x^n/[Product_{k=1..n+1} (1-2^k*x)];
contrast with:
1 = Sum_{n>=0} 2^(n*(n+1)/2) * x^n/[Product_{k=1..n+1} (1+2^k*x)]. (End)
a(n) ~ c * 2^(n*(n+1)/2), where c = A081845. - Vaclav Kotesovec, Dec 31 2015
MAPLE
a[0]:=1: for n from 1 to 16 do a[n]:=(2^n+2)*a[n-1] od: seq(a[n], n=0..16); # Emeric Deutsch, Dec 10 2004
MATHEMATICA
RecurrenceTable[{a[0]==1, a[n]==(2^n + 2) a[n-1]}, a[n], {n, 0, 25}] (* Vincenzo Librandi, Dec 31 2015 *)
PROG
(PARI) {a(n)=polcoeff(sum(m=0, n, 2^(m*(m+1)/2)*x^m/prod(k=1, m+1, 1-2^k*x+x*O(x^n))), n)} \\ Paul D. Hanna, Sep 16 2009
(PARI) a(n) = prod(k=1, n, 2+2^k); \\ Michel Marcus, Jan 01 2016
(Magma) I:=[4]; [1] cat [n le 1 select I[n] else (2^n + 2)*Self(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 31 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, John Leech
EXTENSIONS
More terms from Emeric Deutsch, Dec 10 2004
Replaced arXiv URL with non-cached version - R. J. Mathar, Oct 23 2009
STATUS
approved