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.
%I A027865 #55 Sep 15 2022 02:23:37
%S A027865 55,91,139,199,271,355,451,559,679,811,955,1111,1279,1459,1651,1855,
%T A027865 2071,2299,2539,2791,3055,3331,3619,3919,4231,4555,4891,5239,5599,
%U A027865 5971,6355,6751,7159,7579,8011,8455,8911,9379,9859,10351,10855,11371,11899,12439,12991
%N A027865 Sums of six consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2.
%C A027865 From _Jean-Christophe Hervé_, Nov 11 2015: (Start)
%C A027865 a(n) is defined for n < 0 and a(-n) = a(n-5) for any n; a(-4) = a(-1) = 31, a(-3) = a(-2) = 19.
%C A027865 a(n) == 3 (mod 4) for all n in Z, hence a(n) is never square.
%C A027865 (End)
%H A027865 Vincenzo Librandi, <a href="/A027865/b027865.txt">Table of n, a(n) for n = 0..1000</a>
%H A027865 Patrick De Geest, <a href="http://www.worldofnumbers.com/index.html">World!Of Numbers</a>.
%H A027865 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%H A027865 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>.
%F A027865 a(n) = 6*n^2 + 30*n + 55.
%F A027865 G.f.: (55 - 74*x + 31*x^2) / (1-x)^3. - _R. J. Mathar_, Jun 11 2013
%F A027865 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 12*(n+2). - _Jean-Christophe Hervé_, Nov 11 2015
%F A027865 E.g.f.: (55 + 36*x + 6*x^2)*exp(x). - _G. C. Greubel_, Aug 25 2022
%F A027865 Sum_{n>=0} 1/a(n) = tanh(sqrt(35/3)*Pi/2)*Pi/(2*sqrt(105)) - 50/589. - _Amiram Eldar_, Sep 15 2022
%p A027865 A027865:=n->6*n^2 + 30*n + 55: seq(A027865(n), n=0..60); # _Wesley Ivan Hurt_, Nov 12 2015
%t A027865 Table[Total@ Map[#^2 &, n + Range[0, 5]], {n, 0, 34}] (* _Michael De Vlieger_, Nov 12 2015 *)
%t A027865 Total/@Partition[Range[0,40]^2,6,1] (* or *) Table[6x^2+30x+55,{x,0,40}] (* _Harvey P. Dale_, Mar 23 2018 *)
%o A027865 (PARI) a(n)=6*n^2+30*n+55 \\ _Charles R Greathouse IV_, Jul 28 2015
%o A027865 (PARI) Vec((-31*x^2+74*x-55)/(x-1)^3 + O(x^50)) \\ _Altug Alkan_, Nov 12 2015
%Y A027865 Cf. A000290, A001844, A027575, A027578, A120328, A260637, A276026.
%K A027865 nonn,easy
%O A027865 0,1
%A A027865 _Patrick De Geest_
%E A027865 Corrected by _Ralf Stephan_, Jan 02 2005
%E A027865 Edited by _Charles R Greathouse IV_, Jul 25 2010
%E A027865 Renamed by _Jean-Christophe Hervé_, Nov 12 2015