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A093907 Number of elements in the n-th period of the periodic table as predicted by the Aufbau principle. 18


%S 2,8,8,18,18,32,32,50,50,72,72,98,98,128,128,162,162,200,200,242,242,

%T 288,288,338,338,392,392,450,450,512,512,578,578,648,648,722,722,800,

%U 800,882,882,968,968,1058,1058,1152,1152,1250,1250,1352,1352,1458,1458

%N Number of elements in the n-th period of the periodic table as predicted by the Aufbau principle.

%C Maximum number of electrons in the n-th shell of an atom. - _Daniel Forgues_, May 09 2011

%D Restrepo, G. and Pachon, L., Pythagoras and the Periodic Table, Journal of Chemical Education, submitted, 2004.

%H Harry J. Smith, <a href="/A093907/b093907.txt">Table of n, a(n) for n = 1..20000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Aufbau_principle">Aufbau principle</a>

%H M. Winter, <a href="http://www.webelements.com/webelements/scholar/index.html">WebElements Periodic Table</a>

%H <a href="http://jchemed.chem.wisc.edu/Journal/">Journal of Chemical Education</a>

%F a(n) = 2*floor((n+2)/2)^2. - Leonardo Pachon (leaupaco(AT)yahoo.es), Jul 31 2004

%F a(n) = 2*A008794(n+2). G.f.: 2*x*(1+3*x-x^3-2*x^2+x^4)/((1+x)^2*(1-x)^3 ). - _R. J. Mathar_, Oct 04 2009

%F a(n) = (2*n+3+(-1)^n)^2/8, from _Luce ETIENNE_. [_Bruno Berselli_, Jun 03 2014]

%e a(1) = 2: H and He.

%p A093907:=n->(2*n+3+(-1)^n)^2/8: seq(A093907(n), n=1..100); # _Wesley Ivan Hurt_, Jan 10 2017

%t Table[(2 n + 3 + (-1)^n)^2/8, {n, 60}] (* _Bruno Berselli_, Jun 03 2014 *)

%o (PARI) {for (n=1, 20000, a=2*floor((n+2)/2)^2; write("b093907.txt", n, " ", a); )} \\ _Harry J. Smith_, Jun 17 2009

%o (MAGMA) [(2*n+3+(-1)^n)^2/8: n in [1..60]]; // _Vincenzo Librandi_, Mar 01 2016

%o (GAP) List([1..60],n->(2*n+3+(-1)^n)^2/8); # _Muniru A Asiru_, Mar 18 2019

%Y Cf. A008794, A116471.

%Y See A269510 for another version.

%K nonn,easy

%O 1,1

%A Guillermo Restrepo, May 26 2004

%E More terms added by _Harry J. Smith_, Jun 17 2009

%E Definition clarified by _Donghwi Park_, Mar 01 2016

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Last modified December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)