A116471 Values 2*(n -+ 1)^2 sorted.

0, 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

Offset: 1

Author

Lekraj Beedassy, Mar 17 2006

Keywords

• nonn
• easy

Comments

For n>2, consists of entries of A001105(n)=2*n^2 (n>1) that appear twice.

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

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..5000
• Wikipedia, Atomic electron configuration table
• Wikipedia, Periodic table
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A001105, A093907, A016742.

Programs

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

Maple

0,seq(op([2*n^2,2*n^2]),n=1..30); # Muniru A Asiru, Oct 25 2018

Mathematica

Rest@ Flatten@ Table[2 (n #)^2 & /@ {-1, 1}, {n, 0, 27}] (* or *)
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 *)

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

Formula

a(2*n) = A001105(n) for n >= 1.

From Colin Barker, Oct 06 2014: (Start)

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 6.

G.f.: -2*x^2*(x^4 - x^3 - 2*x^2 + 3*x + 1)/((x - 1)^3*(x + 1)^2). (End)

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

a(n) = A001057(n+1) + A000217(n+1) for n > 1. - Andrew S. Plewe, Sep 24 2018

E.g.f.: (x*(3 + x)*cosh(x) + (1 + x + x^2)*sinh(x) - 4*x)/2. - Stefano Spezia, Aug 13 2022

Extensions

More terms from Joshua Zucker, May 11 2006