A138377 a(0) = 0, a(1) = 1, a(2) = 3, a(3) = 2; thereafter a(n) = -4*a(n-4).

0, 1, 3, 2, 0, -4, -12, -8, 0, 16, 48, 32, 0, -64, -192, -128, 0, 256, 768, 512, 0, -1024, -3072, -2048, 0, 4096, 12288, 8192, 0, -16384, -49152, -32768, 0, 65536, 196608, 131072, 0, -262144, -786432, -524288, 0, 1048576, 3145728, 2097152, 0, -4194304, -12582912, -8388608, 0, 16777216, 50331648

Offset: 0

Author

Paul Curtz, May 08 2008

Keywords

• sign
• easy

Comments

First and third differences have only 2^n's.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, -4).

Crossrefs

Cf. A138380, A138382.

Programs

Mathematica

LinearRecurrence[{0,0,0,-4},{0,1,3,2},60] (* Harvey P. Dale, Mar 19 2012 *)

PARI

x='x+O('x^25); Vec(x*(1+x)*(2*x+1)/((1-2*x+2*x^2)*(1+2*x+2*x^2))) \\ G. C. Greubel, Feb 20 2017

Formula

From R. J. Mathar, May 09 2008: (Start)

O.g.f.: x*(1+x)*(2*x+1)/((1-2*x+2*x^2)*(1+2*x+2*x^2)).

a(n) = (5*A009545(n) - A108520(n))/4. (End)