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.

A273220 a(n) = 8n^2 - 12n + 1.

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%I A273220 #29 Jun 26 2016 10:59:08
%S A273220 9,37,81,141,217,309,417,541,681,837,1009,1197,1401,1621,1857,2109,
%T A273220 2377,2661,2961,3277,3609,3957,4321,4701,5097,5509,5937,6381,6841,
%U A273220 7317,7809,8317,8841,9381,9937,10509,11097,11701,12321,12957,13609,14277,14961,15661
%N A273220 a(n) = 8n^2 - 12n + 1.
%C A273220 Sequence may be obtained by starting with the segment (9, 37) followed by the line from 37 in the direction 37, 81,... in the square spiral whose vertices are the generalized hexagonal numbers (A000217). - _Omar E. Pol_, Jun 26 2016
%H A273220 Colin Barker, <a href="/A273220/b273220.txt">Table of n, a(n) for n = 2..1000</a>
%H A273220 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A273220 From _Colin Barker_, May 18 2016: (Start)
%F A273220 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>4.
%F A273220 G.f.: x^2*(9+10*x-3*x^2) / (1-x)^3.
%F A273220 (End)
%t A273220 Table[8 n^2 - 12 n + 1, {n, 2, 45}] (* or *)
%t A273220 Drop[#, 2] &@ CoefficientList[Series[x^2 (9 + 10 x - 3 x^2)/(1 - x)^3, {x, 0, 45}], x] (* _Michael De Vlieger_, Jun 26 2016 *)
%o A273220 (PARI) Vec(x^2*(9+10*x-3*x^2)/(1-x)^3 + O(x^50)) \\ _Colin Barker_, May 18 2016
%K A273220 nonn,easy
%O A273220 2,1
%A A273220 _Dimitri Boscainos_, May 18 2016