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 A103455 #23 Sep 08 2022 08:45:16 %S A103455 1,4,24,124,624,3124,15624,78124,390624,1953124,9765624,48828124, %T A103455 244140624,1220703124,6103515624,30517578124,152587890624, %U A103455 762939453124,3814697265624,19073486328124,95367431640624,476837158203124 %N A103455 a(n) = 0^n + 5^n - 1. %C A103455 A transform of 5^n under the matrix A103452. %H A103455 Vincenzo Librandi, <a href="/A103455/b103455.txt">Table of n, a(n) for n = 0..400</a> %H A103455 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5). %F A103455 G.f.: (1 - 2*x + 5*x^2)/((1-x)*(1-5*x)). %F A103455 a(n) = Sum_{k=0..n} A103452(n, k)*5^k. %F A103455 a(n) = Sum_{k=0..n} (2*0^(n-k) - 1)*0^(k*(n-k))*5^k. %F A103455 a(n) = A024049(n), n > 0. - _R. J. Mathar_, Aug 30 2008 %F A103455 E.g.f.: 1 - exp(x) + exp(5*x). - _G. C. Greubel_, Jun 21 2021 %t A103455 Join[{1},5^Range[20]-1] (* _Harvey P. Dale_, Nov 15 2011 *) %o A103455 (Magma) [0^n+5^n-1: n in [0..30]]; // _Vincenzo Librandi_, Jun 06 2011 %o A103455 (Sage) [1]+[5^n -1 for n in [1..40]] # _G. C. Greubel_, Jun 21 2021 %Y A103455 Cf. A024049, A103452. %K A103455 easy,nonn %O A103455 0,2 %A A103455 _Paul Barry_, Feb 06 2005