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A158302 "1" followed by repeats of 2^k deleting all 4^k, k>0 5
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 (list; graph; refs; listen; history; text; internal format)
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

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: A120544 A155950 A162959 * 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

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Last modified May 18 10:19 EDT 2021. Contains 343995 sequences. (Running on oeis4.)