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 A082412 #22 Apr 25 2025 09:48:03
%S A082412 1,6,44,344,2736,21856,174784,1398144,11184896,89478656,715828224,
%T A082412 5726623744,45812985856,366503878656,2932031012864,23456248070144,
%U A082412 187649984495616,1501199875833856,12009599006408704,96076792050745344,768614336404914176
%N A082412 a(n) = (2*8^n + 2^n)/3.
%C A082412 Binomial transform of A083076.
%H A082412 Nathaniel Johnston, <a href="/A082412/b082412.txt">Table of n, a(n) for n = 0..250</a>
%H A082412 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-16).
%F A082412 G.f.: (1-4*x)/((1-2*x)*(1-8*x));
%F A082412 E.g.f.: (2*exp(8*x) + exp(2*x))/3.
%F A082412 a(n) = (2*8^n + 2^n)/3.
%F A082412 a(n) = 2^n*A001045(2n+1). - _Paul Barry_, Sep 10 2007
%p A082412 seq((2*8^n+2^n)/3,n=0..20); # _Nathaniel Johnston_, Jun 26 2011
%t A082412 Table[(2*8^n+2^n)/3,{n,0,30}] (* or *) LinearRecurrence[{10,-16},{1,6},30] (* _Harvey P. Dale_, Sep 30 2018 *)
%o A082412 (PARI) a(n)=(2*8^n+2^n)/3 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A082412 (Python)
%o A082412 def A082412(n): return (2<<(n<<1)|1)//3<<n # _Chai Wah Wu_, Apr 25 2025
%Y A082412 Cf. A082413.
%K A082412 easy,nonn
%O A082412 0,2
%A A082412 _Paul Barry_, Apr 23 2003