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 A034008 #64 Jan 28 2020 12:32:28
%S A034008 1,0,1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,
%T A034008 65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,
%U A034008 33554432,67108864,134217728,268435456,536870912,1073741824,2147483648
%N A034008 a(n) = floor(2^|n-1|/2). Or: 1, 0, followed by powers of 2.
%C A034008 Powers of 2 with additional first two terms.
%C A034008 Essentially the same as A131577 (and A000079).
%C A034008 [(-1)^n*a(n)] = [1, 0, 1, -2, 4, -8, 16, -32, ...] is the inverse binomial transform of A008619 = [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, ...]. - _Philippe Deléham_, Nov 15 2009
%C A034008 Number of compositions (ordered partitions) of n into an even number of parts. - _Geoffrey Critzer_, Mar 28 2010
%C A034008 Number of compositions of n into an even number of even parts.
%C A034008 Number of compositions of n into parts k >= 2 where there are k - 1 sorts of part k. - _Joerg Arndt_, Sep 30 2012
%C A034008 Taking n-th differences of this sequence reproduces the same sequence except for a(1) = n mod 2 (parity of n) and a(0) = (-1)^a(1)*floor(n/2 + 1). - _M. F. Hasler_, Jan 13 2015
%D A034008 Richard P. Stanley, Enumerative Combinatorics, Vol. I, Cambridge University Press, 1997, p. 45, exercise 9.
%H A034008 G. C. Greubel, <a href="/A034008/b034008.txt">Table of n, a(n) for n = 0..1000</a>
%H A034008 J.-L. Baril, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v18i1p178">Classical sequences revisited with permutations avoiding dotted pattern</a>, Electronic Journal of Combinatorics, 18 (2011), #P178.
%H A034008 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).
%F A034008 a(n) = 2^(n-2), n >= 2; a(0) = 1, a(1) = 0.
%F A034008 G.f.: (1-x)^2/(1-2*x).
%F A034008 G.f. 1/( 1 - Sum_{k >= 1} (k-1)*x^k ). - _Joerg Arndt_, Sep 30 2012
%F A034008 G.f.: x*G(0), where G(k) = 1 + 1/(1 - (1 - x)/(1 + x*(k+1)/G(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Aug 01 2013
%F A034008 a(n+1) = A131577(n) and a(n+2) = A000079(n) for all n >= 0. - _M. F. Hasler_, Jan 13 2015
%F A034008 Inverse binomial transform of (3^n - 2*n + 1)/2 for n >= 0. - _Paul Curtz_, Sep 24 2019
%F A034008 E.g.f.: (1/4)*(3 + exp(2*x) - 2*x). - _Stefano Spezia_, Sep 25 2019
%F A034008 Binomial transform of A001057(n+1) or (-1)^n*A008619(n). - _Paul Curtz_, Oct 07 2019
%p A034008 A034008:=n->2^(n-2): 1, 0, seq(A034008(n), n=2..50); # _Wesley Ivan Hurt_, Apr 12 2017
%t A034008 a = x/(1 - x); CoefficientList[Series[1/(1 - a^2), {x, 0, 30}], x] (* _Geoffrey Critzer_, Mar 28 2010 *)
%o A034008 (PARI) a(n)=if(n<2,n==0,2^(n-2))
%Y A034008 Cf. A011782, A131577, A000079.
%Y A034008 Cf. A001057, A008619.
%K A034008 easy,nonn
%O A034008 0,4
%A A034008 _Wolfdieter Lang_
%E A034008 Additional comments from _Barry E. Williams_, May 27 2000
%E A034008 Additional comments from _Michael Somos_, Jun 18 2002
%E A034008 Edited by _M. F. Hasler_, Jan 13 2015