A198762 a(n) = 3*5^n - 1 = 2*A057651(n).

2, 14, 74, 374, 1874, 9374, 46874, 234374, 1171874, 5859374, 29296874, 146484374, 732421874, 3662109374, 18310546874, 91552734374, 457763671874, 2288818359374, 11444091796874, 57220458984374, 286102294921874, 1430511474609374, 7152557373046874, 35762786865234374

Offset: 0

Author

Vincenzo Librandi, Oct 30 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-5).

Crossrefs

Cf. A024049, A057651, A081655.

Programs

Magma

[(3*5^n-1): n in [0..30]];

Mathematica

CoefficientList[Series[2*(1 + x)/(1 - 6*x + 5*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *)
LinearRecurrence[{6,-5},{2,14},30] (* Harvey P. Dale, Mar 19 2013 *)

Formula

a(n) = 5*a(n-1) + 4.

a(n) = 6*a(n-1) - 5*a(n-2), n > 1.

G.f.: 2*(1 + x)/(1 - 6*x + 5*x^2). - Vincenzo Librandi, Jan 04 2013

E.g.f.: exp(x)*(3*exp(4*x) - 1). - Elmo R. Oliveira, Mar 29 2025