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 A270568 #18 Mar 25 2025 20:26:50
%S A270568 1,12,96,768,6144,49152,393216,3145728,25165824,201326592,1610612736,
%T A270568 12884901888,103079215104,824633720832,6597069766656,52776558133248,
%U A270568 422212465065984,3377699720527872,27021597764222976,216172782113783808,1729382256910270464,13835058055282163712
%N A270568 Expansion of g.f. (1+4*x)/(1-8*x).
%C A270568 Partial sums are 1, 13, 109, 877, 7021, 56173, ...
%H A270568 Colin Barker, <a href="/A270568/b270568.txt">Table of n, a(n) for n = 0..1000</a>
%H A270568 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (8).
%F A270568 G.f.: (1+4*x)/(1-8*x).
%F A270568 a(n) = 8*a(n-1) for n>1.
%F A270568 a(n) = 12*8^(n-1) for n>0.
%F A270568 a(n) = A094085(n), n>1. - _R. J. Mathar_, Mar 21 2016
%F A270568 E.g.f.: (3*exp(8*x) - 1)/2. - _Elmo R. Oliveira_, Mar 25 2025
%t A270568 CoefficientList[Series[(1 + 4 x)/(1 - 8 x), {x, 0, 20}], x] (* _Michael De Vlieger_, Mar 19 2016 *)
%t A270568 Join[{1},NestList[8#&,12,30]] (* _Harvey P. Dale_, Oct 05 2022 *)
%o A270568 (PARI) Vec((1+4*x)/(1-8*x) + O(x^30))
%Y A270568 Cf. A001018 (powers of 8), A094085, A204623.
%K A270568 nonn,easy
%O A270568 0,2
%A A270568 _Colin Barker_, Mar 19 2016