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.

A108100 a(n) = (2*n-1)^2 + (2*n+1)^2.

This page as a plain text file.
%I A108100 #34 Nov 16 2024 20:15:29
%S A108100 2,10,34,74,130,202,290,394,514,650,802,970,1154,1354,1570,1802,2050,
%T A108100 2314,2594,2890,3202,3530,3874,4234,4610,5002,5410,5834,6274,6730,
%U A108100 7202,7690,8194,8714,9250,9802,10370,10954,11554,12170,12802,13450,14114,14794,15490
%N A108100 a(n) = (2*n-1)^2 + (2*n+1)^2.
%H A108100 Vincenzo Librandi, <a href="/A108100/b108100.txt">Table of n, a(n) for n = 0..10000</a>
%H A108100 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A108100 From R. J. Mathar, Aug 24 2008: (Start)
%F A108100 O.g.f.: 2*(1 + 2*x + 5*x^2)/(1-x)^3.
%F A108100 a(n) = 2*A053755(n). (End)
%F A108100 a(n) = a(-n); a(n) + a(-n) = A158444(n). - _Bruno Berselli_, Sep 06 2011
%F A108100 a(n) = 2*(A000466(n) + 2). - _Martin Ettl_, Nov 12 2012
%F A108100 From _Elmo R. Oliveira_, Nov 16 2024: (Start)
%F A108100 E.g.f.: 2*exp(x)*(1 + 4*x + 4*x^2).
%F A108100 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A108100 Table[8n^2+2,{n,0,50}]  (* _Harvey P. Dale_, Feb 20 2011 *)
%o A108100 (Magma) [8*n^2+2: n in [0..50]]; // _Vincenzo Librandi_, Sep 06 2011
%o A108100 (Maxima) makelist(8*n^2+2,n,0,30); /* _Martin Ettl_, Nov 12 2012 */
%o A108100 (PARI) a(n)=(2*n-1)^2+(2*n+1)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A108100 Apart from leading term, same as A008527.
%Y A108100 Cf. A000466, A016754, A053755, A158444.
%K A108100 nonn,easy
%O A108100 0,1
%A A108100 Dorthe Roel (dorthe_roel(AT)hotmail.com or dorthe.roel1(AT)skolekom.dk), Jun 07 2005