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A140407
A000225 interleaved with A000051.
1
1, 2, 3, 3, 7, 5, 15, 9, 31, 17, 63, 33, 127, 65, 255, 129, 511, 257, 1023, 513, 2047, 1025, 4095, 2049, 8191, 4097, 16383, 8193, 32767, 16385, 65535, 32769, 131071, 65537, 262143, 131073, 524287, 262145, 1048575, 524289, 2097151, 1048577, 4194303
OFFSET
0,2
FORMULA
a(2n) = A000225(n+1) = A135530(2n) - 1. a(2n+1) = A000051(n) = 1 + A135530(2n+1).
a(n) = -a(n-1) + 2*a(n-2) + 2*a(n-3). a(2n) + a(2n+1) = 3*A000079(n).
O.g.f.: (1 + 3x + 3x^2)/((1+x)*(1-2x^2)). - R. J. Mathar, Jul 08 2008
MATHEMATICA
LinearRecurrence[{-1, 2, 2}, {1, 2, 3}, 50] (* Harvey P. Dale, Apr 03 2013 *)
PROG
(Python)
def A140407(n): return 2 if n == 1 else (1<<(n>>1))|1 if n&1 else -1^(-2<<(n>>1)) # Chai Wah Wu, Dec 21 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul Curtz, Jun 16 2008
EXTENSIONS
Edited and extended by R. J. Mathar, Jul 08 2008
STATUS
approved