STATUS
reviewed
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
Revision History for A007178
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Number of ways to write 1 as ordered sum of n powers of 1/2, allowing repeats.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
LINKS
Jia Huang and Erkko Lehtonen, <a href="https://arxiv.org/abs/2401.15786">Associative-commutative spectra for some varieties of groupoids</a>, arXiv:2401.15786 [math.CO], 2024. See p. 18.
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed
FORMULA
Limit_{n->oo} (a(n)/n!)^{(1/n} has a limit as n diverges, the limit is ) = 1.192674341213466032221288982528755... (see References: "Representation of a 2-power as sum of k 2-powers: the asymptotic behavior").
a(n) = = 4 + (-1)^n (mod 8) when for n > 2 (see References: "Representation of a 2-power as sum of k 2-powers: a recursive formula"). (End)
EXAMPLE
For n=3, the 3 sums are 1/2 + 1/4 + 1/4, 1/4 + 1/2 + 1/4, and 1/4 + 1/4 + 1/2.
AUTHOR
N. J. A. Sloane , _, _Simon Plouffe_, Don Knuth
EXTENSIONS
Minor edits, _ from _Vaclav Kotesovec_, Jul 26 2014
STATUS
proposed
editing
STATUS
editing
proposed
LINKS
D. Chataur and M. Livernet, <a href="https://arxiv.org/abs/math/0209363">Adem-Cartan operads, </a>, arXiv:math/0209363 [math.AT], 2002-2003; Communications in Algebra 33 (2005), 4337-4360.
LINKS
A. Giorgilli, and G. Molteni, <a href="http://dx.doi.org/10.1016/j.jnt.2012.09.013">Representation of a 2-power as sum of k 2-powers: a recursive formula</a>, J. Number Theory 133 (2013), no. 4, 1251-1261.
J. Ježek, and T. Kepka, <a href="http://dml.mathdoc.fr/item/106070/">Free entropic groupoids</a>, Commentationes Mathematicae Universitatis Carolinae,Tome 022 (1981), p. 223-233.