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A093907 Number of elements in the n-th period of the periodic table as predicted by the Aufbau principle. 18
2, 8, 8, 18, 18, 32, 32, 50, 50, 72, 72, 98, 98, 128, 128, 162, 162, 200, 200, 242, 242, 288, 288, 338, 338, 392, 392, 450, 450, 512, 512, 578, 578, 648, 648, 722, 722, 800, 800, 882, 882, 968, 968, 1058, 1058, 1152, 1152, 1250, 1250, 1352, 1352, 1458, 1458 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Maximum number of electrons in the n-th shell of an atom. - Daniel Forgues, May 09 2011

REFERENCES

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

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000

Wikipedia, Aufbau principle

M. Winter, WebElements Periodic Table

Journal of Chemical Education

FORMULA

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

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

a(n) = (2*n+3+(-1)^n)^2/8, from Luce ETIENNE. [Bruno Berselli, Jun 03 2014]

EXAMPLE

a(1) = 2: H and He.

MAPLE

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

MATHEMATICA

Table[(2 n + 3 + (-1)^n)^2/8, {n, 60}] (* Bruno Berselli, Jun 03 2014 *)

PROG

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

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

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

CROSSREFS

Cf. A008794, A116471.

See A269510 for another version.

Sequence in context: A104537 A019240 A269510 * A116471 A146749 A250313

Adjacent sequences:  A093904 A093905 A093906 * A093908 A093909 A093910

KEYWORD

nonn,easy

AUTHOR

Guillermo Restrepo, May 26 2004

EXTENSIONS

More terms added by Harry J. Smith, Jun 17 2009

Definition clarified by Donghwi Park, Mar 01 2016

STATUS

approved

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Last modified November 15 01:15 EST 2019. Contains 329142 sequences. (Running on oeis4.)