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

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

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,4,4).

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

From R. J. Mathar, Jun 15 2009: (Start)

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)). (End)

a(n) = (5*(-2)^n-40*(-1)^n+2^n)/8 for n > 0. - Harvey P. Dale, Jun 10 2011

Mathematica

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

Prog

(Magma) [2^(n-2)+5*(-1)^n*(1-2^(n-2)): n in [0..40]]; // Vincenzo Librandi, Aug 09 2011
(PARI) a(n)=if(n, (2^n-5*(-2)^n)/4+5*(-1)^n, 4) \\ Charles R Greathouse IV, Jun 03 2026

Crossrefs

Cf. A137241, A135529, A135520.

Sequence in context: A245324 A039962 A046741 * A142147 A291977 A142073

Adjacent sequences: A136246 A136247 A136248 * A136250 A136251 A136252

Keyword

sign,easy

Author

Paul Curtz, Mar 17 2008

Extensions

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

More terms from Harvey P. Dale, Jun 10 2011

Name edited by Michel Marcus, Jun 03 2026

Status

approved