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"1" followed by repeats of 2^k deleting all 4^k, k>0
5

%I #31 Jun 30 2023 00:42:41

%S 1,2,2,8,8,32,32,128,128,512,512,2048,2048,8192,8192,32768,32768,

%T 131072,131072,524288,524288,2097152,2097152,8388608,8388608,33554432,

%U 33554432,134217728,134217728,536870912,536870912,2147483648,2147483648,8589934592

%N "1" followed by repeats of 2^k deleting all 4^k, k>0

%C Binomial transform = A122983: (1, 3, 7, 21, 61, 183,...). Equals right border of triangle A158301.

%C 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BlackBishopGraph.html">Black Bishop Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphAutomorphism.html">Graph Automorphism</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WhiteBishopGraph.html">White Bishop Graph</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 4).

%F 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 For n > 3: a(n) = a(n-1)*a(n-2)/a(n-3). [_Reinhard Zumkeller_, Mar 06 2011]

%F For n > 3: a(n) = 4a(n-2). [_Charles R Greathouse IV_, Feb 06 2011]

%F a(n) = Sum_{k, 0<=k<=n} A154388(n,k)*2^k. - _Philippe Deléham_, Dec 17 2011

%F G.f.: (1+2*x-2*x^2)/(1-4*x^2). - _Philippe Deléham_, Dec 17 2011

%e Given "1" followed by repeats of powers of 2: (1, 2, 2, 4, 4, 8, 8, 16, 16,...);

%e delete powers of 4: (4, 16, 64, 156,...) leaving A158300:

%e (1, 2, 2, 8, 8, 32, 32, 128, 128,...).

%p 1,seq(4^floor((n+1)/2)/2, n=1..33); # _Peter Luschny_, Jul 02 2020

%t Join[{1}, Flatten[Table[{2^n, 2^n}, {n, 1, 41, 2}]]] (* _Harvey P. Dale_, Jan 24 2013 *)

%t Join[{1}, Table[2^(2 Ceiling[n/2] - 1), {n, 20}]] (* _Eric W. Weisstein_, Jun 27 2017 *)

%t Join[{1}, 2^(2 Ceiling[Range[20]/2] - 1)] (* _Eric W. Weisstein_, Jun 27 2017 *)

%Y Cf. A122983, A158301, A154388

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Mar 15 2009

%E More terms from _Harvey P. Dale_, Jan 24 2013