cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A271998 Volatile sequence: a(n) = A018227(n)-6.

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%I A271998 #15 Mar 07 2022 16:56:01
%S A271998 30,48,80,112,162,212,284,356,454,552,680,808,970,1132,1332,1532,1774,
%T A271998 2016,2304,2592,2930,3268,3660,4052,4502,4952,5464,5976,6554,7132,
%U A271998 7780,8428,9150,9872,10672,11472,12354,13236,14204,15172,16230,17288,18440
%N A271998 Volatile sequence: a(n) = A018227(n)-6.
%C A271998 Terms up to 112 are the atomic numbers of the elements of group 12 in the periodic table. The group is also known as the volatile metals since almost all elements with that property fall in to group 12.
%H A271998 Colin Barker, <a href="/A271998/b271998.txt">Table of n, a(n) for n = 3..1000</a>
%H A271998 Wikipedia, <a href="https://en.wikipedia.org/wiki/Group_12_element">Group 12 element</a>.
%H A271998 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A271998 From _Colin Barker_, Oct 25 2016: (Start)
%F A271998 G.f.: 2*x^3*(15 - 6*x - 23*x^2 + 12*x^3 + 10*x^4 - 6*x^5)/((1 - x)^4*(1 + x)^2).
%F A271998 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>8.
%F A271998 a(n) = (n^3 + 9*n^2 + 26*n - 24)/6 for n even.
%F A271998 a(n) = (n^3 + 9*n^2 + 29*n - 15)/6 for n odd. (End)
%t A271998 LinearRecurrence[{2,1,-4,1,2,-1},{30,48,80,112,162,212},50] (* _Harvey P. Dale_, Mar 07 2022 *)
%o A271998 (PARI) Vec(2*x^3*(15-6*x-23*x^2+12*x^3+10*x^4-6*x^5)/((1-x)^4*(1+x)^2) + O(x^60)) \\ _Colin Barker_, Oct 25 2016
%K A271998 nonn,easy
%O A271998 3,1
%A A271998 _Natan Arie Consigli_, Jun 27 2016