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.

A014929 a(1)=1, a(n) = n*14^(n-1) + a(n-1).

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%I A014929 #23 May 18 2025 07:56:43
%S A014929 1,29,617,11593,203673,3430617,56137369,899445401,14181546905,
%T A014929 220792014745,3402593219481,51997375255449,789018236134297,
%U A014929 11901025061692313,178581127445062553,2667670656370058137,39692877399129367449,588537118527090893721,8699235348529189004185
%N A014929 a(1)=1, a(n) = n*14^(n-1) + a(n-1).
%H A014929 Vincenzo Librandi, <a href="/A014929/b014929.txt">Table of n, a(n) for n = 1..200</a>
%H A014929 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (29,-224,196).
%F A014929 From _R. J. Mathar_, Mar 05 2008: (Start)
%F A014929 a(n) = (1 + (13*n - 1)*14^n)/169.
%F A014929 O.g.f.: x/((14*x-1)^2*(1-x)). (End)
%F A014929 From _Elmo R. Oliveira_, May 16 2025: (Start)
%F A014929 E.g.f.: exp(x)*(1 + exp(13*x)*(182*x - 1))/169.
%F A014929 a(n) = 28*a(n-1) - 196*a(n-2) + 1 for n > 2.
%F A014929 a(n) = 29*a(n-1) - 224*a(n-2) + 196*a(n-3) for n > 3. (End)
%p A014929 A014929 := proc(n) (1+(13*n-1)*14^n)/169 ; end: seq(A014929(n),n=1..10) ; # _R. J. Mathar_, Mar 05 2008
%t A014929 Table[(1+(13n-1)*14^n)/169, {n, 20}] (* _Wesley Ivan Hurt_, Feb 26 2014 *)
%o A014929 (Magma) [(1+(13*n-1)*14^n)/169: n in [1..20]]; // _Vincenzo Librandi_, Mar 04 2014
%o A014929 (PARI) a(n) = (1+(13*n-1)*14^n)/169; \\ _Jinyuan Wang_, Mar 11 2020
%K A014929 nonn,easy
%O A014929 1,2
%A A014929 _Olivier Gérard_
%E A014929 More terms from _Vincenzo Librandi_, Mar 04 2014