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 A013776 #73 Apr 17 2022 09:22:51
%S A013776 2,32,512,8192,131072,2097152,33554432,536870912,8589934592,
%T A013776 137438953472,2199023255552,35184372088832,562949953421312,
%U A013776 9007199254740992,144115188075855872,2305843009213693952
%N A013776 a(n) = 2^(4*n+1).
%C A013776 a(n) ~ -Pi*E(2*n)/B(2*n), E(n) Euler number, B(n) Bernoulli number. - _Peter Luschny_, Oct 28 2012
%C A013776 Equivalently, powers of 2 with final digit 2. - _Muniru A Asiru_, Mar 15 2019
%C A013776 As phi(a(n)) = (2^n)^4 is a perfect biquadrate (where phi is the Euler totient A000010), this is a subsequence of A078164 and A307690. - _Bernard Schott_, Mar 28 2022
%H A013776 Vincenzo Librandi, <a href="/A013776/b013776.txt">Table of n, a(n) for n = 0..200</a>
%H A013776 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A013776 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A013776 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (16).
%F A013776 From _Philippe Deléham_, Nov 23 2008: (Start)
%F A013776 a(n) = 16*a(n-1), n > 0, a(0) = 2.
%F A013776 G.f.: 2/(1 - 16*x). (End)
%F A013776 From _Peter Bala_, Nov 29 2015: (Start)
%F A013776 a(n) = Sum_{k = 0..n} binomial(2*k,k)*binomial(4*n + 2 - 2*k, 2*n + 1 - k).
%F A013776 Bisection of A264960. (End)
%F A013776 a(n) = A000079(A016813(n)). - _Michel Marcus_, Nov 30 2015
%F A013776 a(n) = Sum_{k = 0..2*n} binomial(4*n + 2, 2*k + 1) = A004171(2*n). - _Peter Bala_, Nov 25 2016
%F A013776 E.g.f.: 2*exp(16*x). - _G. C. Greubel_, Jun 30 2019
%F A013776 From _Bernard Schott_, Apr 15 2022: (Start)
%F A013776 Sum_{n>=0} 1/a(n) = 8/15.
%F A013776 Sum_{n>=0} (-1)^n/a(n) = 8/17. (End)
%e A013776 G.f. = 2 + 32*x + 512*x^2 + 8192*x^3 + 131072*x^4 + 2097152*x^5 + ...
%p A013776 [2^(4*n+1)$n=0..20]; # _Muniru A Asiru_, Apr 10 2019
%t A013776 2^(4*Range[0,20]+1) (* _G. C. Greubel_, Mar 15 2019 *)
%t A013776 NestList[16#&,2,20] (* _Harvey P. Dale_, Jul 28 2019 *)
%o A013776 (Magma) [2^(4*n+1): n in [0..20]]; // _Vincenzo Librandi_, Jun 27 2011
%o A013776 (PARI) a(n)=2<<(4*n) \\ _Charles R Greathouse IV_, Apr 07 2012
%o A013776 (GAP) List([0..20],n->2^(4*n+1)); # _Muniru A Asiru_, Mar 15 2019
%o A013776 (Sage) [2^(4*n+1) for n in (0..20)] # _G. C. Greubel_, Mar 15 2019
%Y A013776 Subsequence of A307690.
%Y A013776 Cf. A000010, A004171, A016813, A264960, A307690.
%Y A013776 Intersection of A000079 and A078164.
%K A013776 nonn,easy
%O A013776 0,1
%A A013776 _N. J. A. Sloane_
%E A013776 Wrong comment deleted by _Kevin Ryde_, Apr 16 2022