A140407 A000225 interleaved with A000051.

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

Author

Paul Curtz, Jun 16 2008

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,2,2).

Crossrefs

Cf. A000051, A000225, A000079, A135530.

Programs

Mathematica

LinearRecurrence[{-1,2,2},{1,2,3},50] (* Harvey P. Dale, Apr 03 2013 *)

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

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

Extensions

Edited and extended by R. J. Mathar, Jul 08 2008