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

0,2

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).

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
(PARI) a(n)=([0, 1, 0; 0, 0, 1; 2, 2, -1]^n*[1; 2; 3])[1, 1] \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Cf. A000051, A000225, A000079, A135530.

Sequence in context: A076557 A394803 A228548 * A063670 A253357 A185909

Adjacent sequences: A140404 A140405 A140406 * A140408 A140409 A140410

Keyword

nonn,easy,changed

Author

Paul Curtz, Jun 16 2008

Extensions

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

Status

approved