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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
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
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Mar 15 2009
EXTENSIONS
More terms from Harvey P. Dale, Jan 24 2013
STATUS
approved