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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 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.)