OFFSET
0,2
COMMENTS
Binomial transform = A122983: (1, 3, 7, 21, 61, 183,...).
Equals right border of triangle A158301.
From Eric W. Weisstein, Jun 27 2017: (Start)
Also the order of the graph automorphism group of the n+1 X n+1 black bishop graph.
For n > 1, also the order of the graph automorphism group of the n X n white bishop graph. (End)
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).
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) = 4*a(n-2). - Charles R Greathouse IV, Feb 06 2011
For n > 3: a(n) = a(n-1)*a(n-2)/a(n-3). - Reinhard Zumkeller, Mar 06 2011
From Philippe Deléham, Dec 17 2011: (Start)
a(n) = Sum_{k, 0<=k<=n} A154388(n,k)*2^k.
G.f.: (1+2*x-2*x^2)/(1-4*x^2). (End)
From Amiram Eldar, Dec 19 2025: (Start)
Sum_{n>=0} 1/a(n) = 7/3.
Sum_{n>=0} (-1)^n/a(n) = 1. (End)
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