A136249 a(n)=-a(n-1)+4*a(n-2)+4*a(n-3).

4, -2, 1, 7, -11, 43, -59, 187, -251, 763, -1019, 3067, -4091, 12283, -16379, 49147, -65531, 196603, -262139, 786427, -1048571, 3145723, -4194299, 12582907, -16777211, 50331643, -67108859, 201326587, -268435451, 805306363, -1073741819, 3221225467

Offset: 0

Author

Paul Curtz, Mar 17 2008

Keywords

• sign

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-1, 4, 4).

Crossrefs

Cf. A137241, A135529.

Programs

Magma

[2^(n-2)+5*(-1)^n*(1-2^(n-2)): n in [0..40]]; // Vincenzo Librandi, Aug 09 2011

Mathematica

LinearRecurrence[{-1,4,4},{4,-2,1},50] (* or *) Table[(5(-2)^n- 40(-1)^n+2^n)/8,{n,50}] (* Harvey P. Dale, Jun 10 2011 *)

Formula

a(2*n)=5-2^(2*n), a(2*n+1)=10-3*a(2n).

a(n)+a(n+1)=A135520(n).

a(n) = 1/6*2^n*a(0) + 1/4*2^n*a(1) - 1/2*a(0)*(-2)^n - 1/3*(-1)^n*a(2) - 1/4*a(1)*(-2)^n + 4/3*(-1)^n*a(0) + 1/4*(-2)^n*a(2) + 1/12*2^n*a(2). - Alexander R. Povolotsky, Mar 31 2008

G.f.: (4+2*x-17*x^2)/((1+2*x)*(1-2*x)*(1+x)). a(n)=2^(n-2)+5*(-1)^n*(1-2^(n-2)). - R. J. Mathar, Jun 15 2009

a(n)=(5*(-2)^n-40*(-1)^n+2^n)/8. - Harvey P. Dale, Jun 10 2011

Extensions

Edited by N. J. A. Sloane, Apr 18 2008

More terms from Harvey P. Dale, Jun 10 2011