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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A116471 Values 2*(n -+ 1)^2 sorted. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

FORMULA

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

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3)- a(n-4) + a(n-5). - Colin Barker, Oct 06 2014

G.f.: -2*x^2*(x^4 - x^3 - 2*x^2 + 3*x + 1) / ((x-1)^3*(x+1)^2). - Colin Barker, Oct 06 2014

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

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 *)

PROG

(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

(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

CROSSREFS

Cf. A001105, A093907, A016742.

Sequence in context: A019240 A269510 A093907 * A146749 A250313 A180825

Adjacent sequences:  A116468 A116469 A116470 * A116472 A116473 A116474

KEYWORD

nonn,easy

AUTHOR

Lekraj Beedassy, Mar 17 2006

EXTENSIONS

More terms from Joshua Zucker, May 11 2006

STATUS

approved

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 December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)