A083229 a(n) = (3*3^n + (-5)^n)/4.

1, 1, 13, -11, 217, -599, 4453, -17891, 102577, -473519, 2485693, -12074171, 61433737, -303980039, 1529466133, -7618632851, 38179257697, -190638008159, 953964881773, -4767499885931, 23844472998457, -119201444285879, 596069983548613, -2980161631385411

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (-2,15)

Formula

G.f.: (1+3*x)/((1-3*x)*(1+5*x)).

E.g.f.: (3*exp(3*x) + exp(-5*x))/4.

a(n) = -2*a(n-1) + 15*a(n-2). - Wesley Ivan Hurt, Dec 29 2023

Mathematica

Table[(3*3^n+(-5)^n)/4, {n, 0, 30}] (* or *) LinearRecurrence[{-2, 15}, {1, 1}, 30] (* Harvey P. Dale, Jun 09 2013 *)

Prog

(Magma) [(3*3^n+(-5)^n)/4: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011

Crossrefs

Sequence in context: A196124 A196121 A298893 * A140554 A356978 A375244

Adjacent sequences: A083226 A083227 A083228 * A083230 A083231 A083232

Keyword

easy,sign

Author

Paul Barry, Apr 23 2003

Status

approved