A084171 Binomial transform of generalized Jacobsthal numbers A084170.

1, 3, 11, 37, 119, 373, 1151, 3517, 10679, 32293, 97391, 293197, 881639, 2649013, 7955231, 23882077, 71678999, 215102533, 645438671, 1936578157, 5810258759, 17431824853, 52297571711, 156896909437, 470699116919, 1412114127973

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,-6)

Formula

a(n) = 5*3^n/3 + 0^n/3 - 2^n.

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

E.g.f.: 5*exp(3*x)/3 - exp(2*x) + exp(0)/3.

a(n) = A090888(n-1, 5), for n > 0. - Ross La Haye, Sep 21 2004

a(n) = 5*a(n-1) - 6*a(n-2). - Wesley Ivan Hurt, May 09 2022

Mathematica

Join[{1}, LinearRecurrence[{5, -6}, {3, 11}, 30]] (* Harvey P. Dale, Jan 20 2014 *)

Prog

(Magma) [5*3^n/3+0^n/3-2^n: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011

Crossrefs

Cf. A084170, A090888.

Sequence in context: A040017 A007615 A065540 * A192875 A118044 A027062

Adjacent sequences: A084168 A084169 A084170 * A084172 A084173 A084174

Keyword

easy,nonn

Author

Paul Barry, May 18 2003

Status

approved