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 A146885 #9 Mar 20 2024 16:18:23 %S A146885 8,64,456,3200,22408,156864,1098056,7686400,53804808,376633664, %T A146885 2636435656,18455049600,129185347208,904297430464,6330082013256, %U A146885 44310574092800,310174018649608,2171218130547264,15198526913830856 %N A146885 a(n) = 8*Sum_{k=0..n} 7^k. %H A146885 G. C. Greubel, <a href="/A146885/b146885.txt">Table of n, a(n) for n = 0..1000</a> %H A146885 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7). %F A146885 From _G. C. Greubel_, Oct 12 2022: (Start) %F A146885 a(n) = (4/3)*(7^(n+1) - 1). %F A146885 a(n) = 8*A023000(n+1). %F A146885 a(n) = 8*a(n-1) - 7*a(n-2). %F A146885 G.f.: 8/((1-x)*(1-7*x)). %F A146885 E.g.f.: (4/3)*(7*exp(7*x) - exp(x)). (End) %t A146885 a[n_]:= Sum[8*7^m, {m,0,n}]; Table[a[n], {n,0,30}] %t A146885 LinearRecurrence[{8,-7}, {8,64}, 41] (* _G. C. Greubel_, Oct 12 2022 *) %o A146885 (Magma) [n le 2 select 8^n else 8*Self(n-1) -7*Self(n-2): n in [1..41]]; // _G. C. Greubel_, Oct 12 2022 %o A146885 (SageMath) [(4/3)*(7^(n+1)-1) for n in range(41)] # _G. C. Greubel_, Oct 12 2022 %Y A146885 Cf. A005843, A023000, A068156, A100774, A132583, A146882, A146883, A146885. %K A146885 nonn,easy,less %O A146885 0,1 %A A146885 _Roger L. Bagula_, Nov 02 2008