A180168 a(n) = 2*a(n-1) + 5*a(n-2), a(0) = 1, a(1) = 3.

1, 3, 11, 37, 129, 443, 1531, 5277, 18209, 62803, 216651, 747317, 2577889, 8892363, 30674171, 105810157, 364991169, 1259033123, 4343022091, 14981209797, 51677530049, 178261109083, 614909868411, 2121125282237, 7316799906529, 25239226224243, 87062451981131

Offset: 0

Author

Gary W. Adamson, Aug 14 2010

Keywords

• nonn
• easy

Examples

			a(5) = 443 = 2*a(4) + 5*a(3) = 2*129 + 5*37.
Using the INVERT operation, a(4) = 129 = (38, 14, 6, 2, 1) dot (1, 1, 3, 11, 37)
= (38 + 14 + 18 + 22 + 37); where A026597 = (1, 2, 6, 14, 38, 94,...).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,5).

Crossrefs

Cf. A026597.

Programs

Mathematica

LinearRecurrence[{2, 5}, {1, 3}, 50] (* G. C. Greubel, Feb 18 2017 *)

PARI

x='x+O('x^25); Vec((1 + x)/(1 - 2*x - 5*x^2)) \\ G. C. Greubel, Feb 18 2017

Formula

G.f.: (1 + x)/(1 - 2*x - 5*x^2).

Equals INVERT transform of A026597: (1, 2, 6, 14, 38, 94,...).

a(n) = (1/6)*( -(1-sqrt(6))^n*sqrt(6) + sqrt(6)*(1+sqrt(6))^n + 3*(1-sqrt(6))^n + 3*(1 +sqrt(6))^n ). - Alexander R. Povolotsky, Aug 15 2010

a(n) = A176812(n)/3 = A002532(n) + A002532(n+1). - R. J. Mathar, Oct 11 2011