A137340 a(n) = 2*a(n-1) + 3*a(n-2), with a(0) = 1, a(1) = 9.

1, 9, 21, 69, 201, 609, 1821, 5469, 16401, 49209, 147621, 442869, 1328601, 3985809, 11957421, 35872269, 107616801, 322850409, 968551221, 2905653669, 8716961001, 26150883009, 78452649021, 235357947069, 706073841201, 2118221523609, 6354664570821, 19063993712469

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,3).

Formula

G.f.: (1 + 7*x)/((1 + x)*(1 - 3*x)). - Andrew Howroyd, Feb 02 2020

From Klaus Purath, Mar 10 2021: (Start)

a(n) = (5*3^n - 3*(-1)^n)/2.

a(2*n) = (5*9^n - 3)/2.

a(2*n+1) = (15*9^n + 3)/2.

a(n) = 20*3^(n-2) + a(n-2), n > 1.

a(n) = A096019(n) - 2*(-1)^n. (End)

Mathematica

LinearRecurrence[{2, 3}, {1, 9}, 30] (* Harvey P. Dale, Jul 31 2023 *)

Prog

(PARI) Vec((1 + 7*x)/((1 + x)*(1 - 3*x)) + O(x^40)) \\ Andrew Howroyd, Feb 02 2020

Crossrefs

Sequence in context: A262055 A193276 A173084 * A075640 A147480 A146396

Adjacent sequences: A137337 A137338 A137339 * A137341 A137342 A137343

Keyword

nonn,easy

Author

Paul Curtz, Apr 21 2008

Extensions

Terms a(10) and beyond from Andrew Howroyd, Feb 02 2020

Status

approved