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 A158302 #34 Jun 02 2025 01:26:41
%S A158302 1,2,2,8,8,32,32,128,128,512,512,2048,2048,8192,8192,32768,32768,
%T A158302 131072,131072,524288,524288,2097152,2097152,8388608,8388608,33554432,
%U A158302 33554432,134217728,134217728,536870912,536870912,2147483648,2147483648,8589934592
%N A158302 "1" followed by repeats of 2^k deleting all 4^k, k>0.
%C A158302 Binomial transform = A122983: (1, 3, 7, 21, 61, 183,...). Equals right border of triangle A158301.
%C A158302 Also the order of the graph automorphism group of the n+1 X n+1 black bishop graph. - _Eric W. Weisstein_, Jun 27 2017
%C A158302 For n > 1, also the order of the graph automorphism group of the n X n white bishop graph. - _Eric W. Weisstein_, Jun 27 2017
%H A158302 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BlackBishopGraph.html">Black Bishop Graph</a>
%H A158302 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphAutomorphism.html">Graph Automorphism</a>
%H A158302 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WhiteBishopGraph.html">White Bishop Graph</a>
%H A158302 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 4).
%F A158302 1 followed by repeats of powers of 2, deleting powers of 4: (4, 16, 64,...). Inverse binomial transform of A122983 starting (1, 3, 7, 21, 61, 183,...).
%F A158302 For n > 3: a(n) = a(n-1)*a(n-2)/a(n-3). [_Reinhard Zumkeller_, Mar 06 2011]
%F A158302 For n > 3: a(n) = 4a(n-2). [_Charles R Greathouse IV_, Feb 06 2011]
%F A158302 a(n) = Sum_{k, 0<=k<=n} A154388(n,k)*2^k. - _Philippe Deléham_, Dec 17 2011
%F A158302 G.f.: (1+2*x-2*x^2)/(1-4*x^2). - _Philippe Deléham_, Dec 17 2011
%e A158302 Given "1" followed by repeats of powers of 2: (1, 2, 2, 4, 4, 8, 8, 16, 16,...);
%e A158302 delete powers of 4: (4, 16, 64, 156,...) leaving A158300:
%e A158302 (1, 2, 2, 8, 8, 32, 32, 128, 128,...).
%p A158302 1,seq(4^floor((n+1)/2)/2, n=1..33); # _Peter Luschny_, Jul 02 2020
%t A158302 Join[{1}, Flatten[Table[{2^n, 2^n}, {n, 1, 41, 2}]]] (* _Harvey P. Dale_, Jan 24 2013 *)
%t A158302 Join[{1}, Table[2^(2 Ceiling[n/2] - 1), {n, 20}]] (* _Eric W. Weisstein_, Jun 27 2017 *)
%t A158302 Join[{1}, 2^(2 Ceiling[Range[20]/2] - 1)] (* _Eric W. Weisstein_, Jun 27 2017 *)
%Y A158302 Cf. A122983, A158301, A154388
%K A158302 nonn,easy
%O A158302 0,2
%A A158302 _Gary W. Adamson_, Mar 15 2009
%E A158302 More terms from _Harvey P. Dale_, Jan 24 2013