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%I #49 Aug 14 2022 02:46:57
%S 0,2,8,8,18,18,32,32,50,50,72,72,98,98,128,128,162,162,200,200,242,
%T 242,288,288,338,338,392,392,450,450,512,512,578,578,648,648,722,722,
%U 800,800,882,882,968,968,1058,1058,1152,1152,1250,1250,1352,1352,1458,1458
%N Values 2*(n -+ 1)^2 sorted.
%C For n>2, consists of entries of A001105(n)=2*n^2 (n>1) that appear twice.
%C The terms a(2)-a(8) give the number of elements in the periods 1-7 of the periodic table of the chemical elements. - _Antti Karttunen_, Aug 14 2008
%H Muniru A Asiru, <a href="/A116471/b116471.txt">Table of n, a(n) for n = 1..5000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Atomic_electron_configuration_table">Atomic electron configuration table</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Periodic_table">Periodic table</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F a(2*n) = A001105(n) for n >= 1.
%F From _Colin Barker_, Oct 06 2014: (Start)
%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 6.
%F G.f.: -2*x^2*(x^4 - x^3 - 2*x^2 + 3*x + 1)/((x - 1)^3*(x + 1)^2). (End)
%F a(n) = (2*n^2 + 2*n - (2*n + 1)*(-1)^n + 1)/4, with n > 1 and a(1) = 0. - _Bruno Berselli_, Oct 07 2014
%F a(n) = A001057(n+1) + A000217(n+1) for n > 1. - _Andrew S. Plewe_, Sep 24 2018
%F E.g.f.: (x*(3 + x)*cosh(x) + (1 + x + x^2)*sinh(x) - 4*x)/2. - _Stefano Spezia_, Aug 13 2022
%p 0,seq(op([2*n^2,2*n^2]),n=1..30); # _Muniru A Asiru_, Oct 25 2018
%t Rest@ Flatten@ Table[2 (n #)^2 & /@ {-1, 1}, {n, 0, 27}] (* or *)
%t Rest@ CoefficientList[Series[-2 x^2 (x^4 - x^3 - 2 x^2 + 3 x + 1)/((x - 1)^3 (x + 1)^2), {x, 0, 54}], x] (* _Michael De Vlieger_, Jul 22 2016 *)
%o (PARI) concat(0, Vec(-2*x^2*(x^4-x^3-2*x^2+3*x+1)/((x-1)^3*(x+1)^2) + O(x^100))) \\ _Colin Barker_, Oct 06 2014
%o (GAP) a:=[2,8,8,18,18];; for n in [6..54] do a[n]:=a[n-1]+2*a[n-2]-2*a[n-3]-a[n-4]+a[n-5]; od; Concatenation([0],a); # _Muniru A Asiru_, Oct 25 2018
%Y Cf. A001105, A093907, A016742.
%K nonn,easy
%O 1,2
%A _Lekraj Beedassy_, Mar 17 2006
%E More terms from _Joshua Zucker_, May 11 2006
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