A120656 a(n) = (-4 + (-2)^n + 2*3^(n+1))/3 - [n=0].

0, 4, 18, 50, 166, 474, 1478, 4330, 13206, 39194, 118438, 353610, 1064246, 3185914, 9571398, 28686890, 86115286, 258236634, 774928358, 2324348170, 6973918326, 20920007354, 62763517318, 188283561450, 564864665366, 1694566034074

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,5,-6).

Formula

From Colin Barker, Oct 19 2012: (Start)

a(n) = (-4 + (-2)^n + 2*3^(n+1))/3 - [n=0].

a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3) for n>3.

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

E.g.f.: (1/3)*(exp(-2*x) - 3 - 4*exp(x) + 6*exp(3*x)). - G. C. Greubel, Dec 25 2022

Mathematica

LinearRecurrence[{2, 5, -6}, {0, 4, 18, 50}, 51] (* Harvey P. Dale, Oct 18 2014 *)

Prog

(Magma) [0] cat [(-4 + (-2)^n + 2*3^(n+1))/3: n in [1..50]]; // G. C. Greubel, Dec 25 2022
(SageMath) [(-4 + (-2)^n + 2*3^(n+1))/3 -int(n==0) for n in range(51)] # G. C. Greubel, Dec 25 2022

Crossrefs

Cf. A120655.

Sequence in context: A353162 A303737 A180805 * A256431 A256430 A225263

Adjacent sequences: A120653 A120654 A120655 * A120657 A120658 A120659

Keyword

nonn,less

Author

Roger L. Bagula, Aug 10 2006

Extensions

Edited by G. C. Greubel, Dec 25 2022

Meaningful name using given formula from Joerg Arndt, Dec 26 2022

Status

approved