A138322 a(n) = 5*a(n-1) + 10*a(n-2).

1, 15, 85, 575, 3725, 24375, 159125, 1039375, 6788125, 44334375, 289553125, 1891109375, 12351078125, 80666484375, 526843203125, 3440880859375, 22472836328125, 146772990234375, 958593314453125, 6260696474609375

Offset

0,2

Comments

a(n)/a(n-1) tends to 6.53112887... = (5 + sqrt(65))/2

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (5,10).

Formula

a(n), n>1 = 5*a(n-1) + 10*a(n-2), given a(0) = 1, a(1) = 15. [a(n), a(n+1)] = the 2 X 2 matrix [0,1; 10,5]^n * [1,15]

O.g.f.: (-1-10*x)/(-1+5*x+10*x^2). - R. J. Mathar, Mar 15 2008

Example

a(5) = 24375 = 5*a(4) + 10*a(3) = 5*3725 + 10*575.
[a(3), a(4)] = [575,3725] = [0,1; 10,5]^3 * [1,15].

Mathematica

LinearRecurrence[{5, 10}, {1, 15}, 30] (* Harvey P. Dale, Jan 28 2021 *)

Crossrefs

Sequence in context: A176070 A160747 A064058 * A206170 A177882 A199897

Adjacent sequences: A138319 A138320 A138321 * A138323 A138324 A138325

Keyword

nonn,easy

Author

Gary W. Adamson, Mar 14 2008

Extensions

Corrected and extended by R. J. Mathar, Mar 15 2008

Status

approved