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 A100705 #36 Apr 20 2025 09:03:52
%S A100705 1,5,17,43,89,161,265,407,593,829,1121,1475,1897,2393,2969,3631,4385,
%T A100705 5237,6193,7259,8441,9745,11177,12743,14449,16301,18305,20467,22793,
%U A100705 25289,27961,30815,33857,37093,40529,44171,48025,52097,56393,60919,65681,70685,75937
%N A100705 a(n) = n^3 + (n+1)^2.
%C A100705 The finite simple continued fraction [1;n-1,n,n+1] has a numerator in the resulting rational number (n^3+2*n+n^2+1)/(n*(n^2+1)) that is the same as a(n). - _J. M. Bergot_, Sep 29 2011
%H A100705 Vincenzo Librandi, <a href="/A100705/b100705.txt">Table of n, a(n) for n = 0..10000</a>
%H A100705 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A100705 G.f.: (1+x+3*x^2+x^3)/(x-1)^4. - _R. J. Mathar_, Sep 29 2011
%F A100705 a(n) = A053698(n) + n. - _Bruno Berselli_, Sep 30 2011
%F A100705 From _Elmo R. Oliveira_, Apr 19 2025: (Start)
%F A100705 E.g.f.: exp(x)*(1 + x)*(1 + 3*x + x^2).
%F A100705 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%t A100705 Table[n^3 + (n + 1)^2, {n, 0, 45}]
%t A100705 LinearRecurrence[{4,-6,4,-1},{1,5,17,43},50] (* _Harvey P. Dale_, Dec 03 2014 *)
%o A100705 (Magma) [n^3 + (n+1)^2: n in [0..50]]; // _Vincenzo Librandi_, Sep 30 2011
%o A100705 (PARI) a(n)=n^3+(n+1)^2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A100705 Cf. A053698.
%K A100705 nonn,easy
%O A100705 0,2
%A A100705 _Giovanni Teofilatto_, Jan 03 2005
%E A100705 More terms from Mark Hudson and _Farideh Firoozbakht_, Jan 04 2005