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
Examples
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,...).
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
- Index entries for linear recurrences with constant coefficients, signature (0, 4).
Programs
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Maple
1,seq(4^floor((n+1)/2)/2, n=1..33); # Peter Luschny, Jul 02 2020
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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 *)
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
Extensions
More terms from Harvey P. Dale, Jan 24 2013
Comments