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 A083885 #15 Jun 02 2025 00:15:54
%S A083885 1,1,6,16,72,256,1056,4096,16512,65536,262656,1048576,4196352,
%T A083885 16777216,67117056,268435456,1073774592,4294967296,17180000256,
%U A083885 68719476736,274878431232,1099511627776,4398048608256,17592186044416,70368752566272
%N A083885 (4^n+2^n+0^n+(-2)^n)/4.
%C A083885 Binomial transform of A083884.
%H A083885 Vincenzo Librandi, <a href="/A083885/b083885.txt">Table of n, a(n) for n = 0..200</a>
%H A083885 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,4,-16).
%F A083885 a(n) = (4^n+2^n+0^n+(-2)^n)/4.
%F A083885 G.f.: (4*x^3-2*x^2-3*x+1)/((2*x+1)*(2*x-1)*(4*x-1)).
%F A083885 E.g.f.: exp(4*x)+exp(2*x)+exp(0)+exp(-2*x).
%F A083885 A007814(a(n)) = A022998(n-1). - _Ralf Stephan_, Feb 14 2004
%F A083885 a(0)=1, a(1)=1, a(2)=6, a(3)=16, a(n)=4*a(n-1)+4*a(n-2)-16*a(n-3) [From _Harvey P. Dale_, Dec 12 2011]
%t A083885 Join[{1},Table[(4^n+2^n+(-2)^n)/4,{n,30}]] (* or *) Join[{1}, LinearRecurrence[ {4,4,-16},{1,6,16},30]] (* _Harvey P. Dale_, Dec 12 2011 *)
%o A083885 (Magma) [(4^n+2^n+0^n+(-2)^n)/4: n in [0..20]]; // _Vincenzo Librandi_, Jun 16 2011
%K A083885 easy,nonn
%O A083885 0,3
%A A083885 _Paul Barry_, May 09 2003