A167784 a(n) = 2^n - (1 - (-1)^n)*3^((n-1)/2).

1, 0, 4, 2, 16, 14, 64, 74, 256, 350, 1024, 1562, 4096, 6734, 16384, 28394, 65536, 117950, 262144, 484922, 1048576, 1979054, 4194304, 8034314, 16777216, 32491550, 67108864, 131029082, 268435456, 527304974, 1073741824, 2118785834, 4294967296, 8503841150

Offset: 0

Author

Paul Curtz, Nov 12 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A077917, the signed variant of A127864.

Links

• Robert Israel, Table of n, a(n) for n = 0..3318
• Index entries for linear recurrences with constant coefficients, signature (2,3,-6).

Crossrefs

Cf. A154383.

Programs

Maple

seq(2^n - (1 - (-1)^n)*3^((n-1)/2), n=0..100); # Robert Israel, Apr 11 2019

Mathematica

LinearRecurrence[{2, 3, -6}, {1, 0, 4}, 40] (* Harvey P. Dale, Nov 29 2011 *)

Formula

a(n) = A167936(n+1) - A167936(n).

a(2n) = A000302(n). a(2n+1) = 2*A005061(n).

a(n) = 2*a(n-1) + 3*a(n-2) - 6*a(n-3).

G.f.: (x-1)^2/((2*x-1)*(3*x^2-1)).

a(n+4) mod 9 = A153130(n+4) = A146501(n+2), n>=0.

E.g.f.: exp(2*x) - (2/sqrt(3))*sinh(sqrt(3)*x). - G. C. Greubel, Jun 27 2016

Extensions

Edited and extended by R. J. Mathar, Feb 27 2010

Incorrect b-file corrected by Robert Israel, Apr 11 2019