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.

A103458 a(n) = 7^n + 1 - 0^n.

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%I A103458 #18 Sep 08 2022 08:45:16
%S A103458 1,8,50,344,2402,16808,117650,823544,5764802,40353608,282475250,
%T A103458 1977326744,13841287202,96889010408,678223072850,4747561509944,
%U A103458 33232930569602,232630513987208,1628413597910450,11398895185373144
%N A103458 a(n) = 7^n + 1 - 0^n.
%C A103458 a(n)^3 is palindromic in base 7 (1_7, 1331_7, 1030301_7, 1003003001_7, ...).
%H A103458 G. C. Greubel, <a href="/A103458/b103458.txt">Table of n, a(n) for n = 0..1000</a>
%H A103458 Patrick De Geest, <a href="http://www.worldofnumbers.com/index.html">World!Of Numbers</a>
%H A103458 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).
%F A103458 G.f.: (1-7*x^2)/((1-x)*(1-7*x)).
%F A103458 a(n) = Sum_{k=0..n} binomial(n, k)*0^(k(n-k))*7^k.
%F A103458 a(n) = A034491(n), n > 0. - _R. J. Mathar_, Aug 28 2008
%F A103458 a(n) = 7*a(n-1) - 6, with a(1)=8. - _Vincenzo Librandi_, Dec 29 2010
%F A103458 E.g.f.: -1 + exp(x) + exp(7*x). - _G. C. Greubel_, Jun 22 2021
%t A103458 Table[7^n +1 -Boole[n==0], {n,0,30}] (* _G. C. Greubel_, Jun 22 2021 *)
%o A103458 (Magma) [1] cat [7^n + 1: n in [1..30]]; // _G. C. Greubel_, Jun 22 2021
%o A103458 (Sage) [1]+[7^n + 1 for n in (1..30)] # _G. C. Greubel_, Jun 22 2021
%Y A103458 Cf. A034491, A046233.
%K A103458 easy,nonn
%O A103458 0,2
%A A103458 _Paul Barry_, Feb 07 2005