A158302 "1" followed by repeats of 2^k deleting all 4^k, k>0

1, 2, 2, 8, 8, 32, 32, 128, 128, 512, 512, 2048, 2048, 8192, 8192, 32768, 32768, 131072, 131072, 524288, 524288, 2097152, 2097152, 8388608, 8388608, 33554432, 33554432, 134217728, 134217728, 536870912, 536870912, 2147483648, 2147483648, 8589934592

Offset

0,2

Comments

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

Also the order of the graph automorphism group of the n+1 X n+1 black bishop graph. - Eric W. Weisstein, Jun 27 2017

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

Links

Table of n, a(n) for n=0..33.

Eric Weisstein's World of Mathematics, Black Bishop Graph

Eric Weisstein's World of Mathematics, Graph Automorphism

Eric Weisstein's World of Mathematics, White Bishop Graph

Index entries for linear recurrences with constant coefficients, signature (0, 4).

Formula

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,...).

For n > 3: a(n) = a(n-1)*a(n-2)/a(n-3). [Reinhard Zumkeller, Mar 06 2011]

For n > 3: a(n) = 4a(n-2). [Charles R Greathouse IV, Feb 06 2011]

a(n) = Sum_{k, 0<=k<=n} A154388(n,k)*2^k. - Philippe Deléham, Dec 17 2011

G.f.: (1+2*x-2*x^2)/(1-4*x^2). - Philippe Deléham, Dec 17 2011

Example

Given "1" followed by repeats of powers of 2: (1, 2, 2, 4, 4, 8, 8, 16, 16,...);
delete powers of 4: (4, 16, 64, 156,...) leaving A158300:
(1, 2, 2, 8, 8, 32, 32, 128, 128,...).

Maple

1, seq(4^floor((n+1)/2)/2, n=1..33); # Peter Luschny, Jul 02 2020

Mathematica

Join[{1}, Flatten[Table[{2^n, 2^n}, {n, 1, 41, 2}]]] (* Harvey P. Dale, Jan 24 2013 *)
Join[{1}, Table[2^(2 Ceiling[n/2] - 1), {n, 20}]] (* Eric W. Weisstein, Jun 27 2017 *)
Join[{1}, 2^(2 Ceiling[Range[20]/2] - 1)] (* Eric W. Weisstein, Jun 27 2017 *)

Crossrefs

Cf. A122983, A158301, A154388

Sequence in context: A155950 A162959 A354830 * A007083 A281019 A325513

Adjacent sequences: A158299 A158300 A158301 * A158303 A158304 A158305

Keyword

nonn,easy

Author

Gary W. Adamson, Mar 15 2009

Extensions

More terms from Harvey P. Dale, Jan 24 2013

Status

approved