login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005886 Theta series of f.c.c. lattice with respect to tetrahedral hole.
(Formerly M3429)
6

%I M3429

%S 4,12,12,16,24,12,24,36,12,28,36,24,36,36,24,24,60,36,28,48,12,60,60,

%T 24,48,48,36,48,60,24,52,84,48,24,60,36,48,96,36,72,48,36,72,60,48,52,

%U 96,36,60,96,24,72,108,24,48,60,72,96,84,60,48,108,36,52,72,60,108,108,36,48,108

%N Theta series of f.c.c. lattice with respect to tetrahedral hole.

%C Empirically, the number of integral quadruples with sum = 1, sum-of-squares = 2n-1. - _Colin Mallows_, Dec 31 2016

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H G. C. Greubel, <a href="/A005886/b005886.txt">Table of n, a(n) for n = 0..1000</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/D3.html">Home page for this lattice</a>

%H N. J. A. Sloane and B. K. Teo, <a href="http://dx.doi.org/10.1063/1.449551">Theta series and magic numbers for close-packed spherical clusters</a>, J. Chem. Phys. 83 (1985) 6520-6534.

%H <a href="/index/Fa#fcc">Index entries for sequences related to f.c.c. lattice</a>

%F a(n) = 1/2 * A005878(n) = 2 * A005869(n) = 4 * A008443(n). - _Michael Somos_, May 31 2012

%e 4 + 12*x + 12*x^2 + 16*x^3 + 24*x^4 + 12*x^5 + 24*x^6 + 36*x^7 + 12*x^8 + ...

%t QP = QPochhammer; CoefficientList[4(QP[q^2]^2/QP[q])^3 + O[q]^50, q] (* _Jean-Fran├žois Alcover_, Jul 04 2017, after _Michael Somos_ *)

%Y Cf. A005869, A005878, A008443. Partial sums is A121054. Cf also A278081-A278086.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

%E Terms a(50) onward added by _G. C. Greubel_, Feb 20 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 00:12 EST 2019. Contains 329310 sequences. (Running on oeis4.)