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.

A271995 The Pnictogen sequence: a(n) = A018227(n)-3.

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%I A271995 #20 Oct 29 2023 16:45:36
%S A271995 7,15,33,51,83,115,165,215,287,359,457,555,683,811,973,1135,1335,1535,
%T A271995 1777,2019,2307,2595,2933,3271,3663,4055,4505,4955,5467,5979,6557,
%U A271995 7135,7783,8431,9153,9875,10675,11475,12357,13239,14207,15175,16233,17291,18443
%N A271995 The Pnictogen sequence: a(n) = A018227(n)-3.
%C A271995 Terms up to 115 are the atomic numbers of the elements of group 15 in the periodic table. Those elements are also known as pnictogens.
%H A271995 Colin Barker, <a href="/A271995/b271995.txt">Table of n, a(n) for n = 2..1000</a>
%H A271995 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pnictogen">Pnictogen</a>.
%H A271995 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A271995 From _Colin Barker_, Jun 19 2016, corrected Jun 26 2016: (Start)
%F A271995 a(n) = (6*(-7+(-1)^n)+(25+3*(-1)^n)*n+12*n^2+2*n^3)/12.
%F A271995 a(n) = (n^3+6*n^2+14*n-18)/6 for n even.
%F A271995 a(n) = (n^3+6*n^2+11*n-24)/6 for n odd.
%F A271995 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>7.
%F A271995 G.f.: x^2*(7+x-4*x^2-2*x^3+x^4+x^5) / ((1-x)^4*(1+x)^2).
%F A271995 (End)
%t A271995 LinearRecurrence[{2,1,-4,1,2,-1},{7,15,33,51,83,115},50] (* _Harvey P. Dale_, Oct 29 2023 *)
%o A271995 (PARI) Vec(x^2*(7+x-4*x^2-2*x^3+x^4+x^5)/((1-x)^4*(1+x)^2) + O(x^100)) \\ _Colin Barker_, Jun 19 2016, corrected Jun 26 2016
%Y A271995 Cf. A018227.
%K A271995 nonn,easy
%O A271995 2,1
%A A271995 _Natan Arie Consigli_, Jun 18 2016