A198766 a(n) = (7*5^n - 1)/2.

3, 17, 87, 437, 2187, 10937, 54687, 273437, 1367187, 6835937, 34179687, 170898437, 854492187, 4272460937, 21362304687, 106811523437, 534057617187, 2670288085937, 13351440429687, 66757202148437, 333786010742187, 1668930053710937

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

[(7*5^n-1)/2: n in [0..30]];

Mathematica

CoefficientList[Series[(3 - x)/(1 - 6*x + 5*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *)
LinearRecurrence[{6,-5},{3,17},30] (* Harvey P. Dale, Jan 23 2015 *)

Formula

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

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

G.f.: (3 - x)/(1 - 6*x + 5*x^2). - Vincenzo Librandi, Jan 04 2013

E.g.f.: exp(x)*(7*exp(4*x) - 1)/2. - Stefano Spezia, Mar 08 2025