A198964 a(n) = (7*9^n - 1)/2.

3, 31, 283, 2551, 22963, 206671, 1860043, 16740391, 150663523, 1355971711, 12203745403, 109833708631, 988503377683, 8896530399151, 80068773592363, 720618962331271, 6485570660981443, 58370135948832991, 525331223539496923

Offset: 0

Author

Vincenzo Librandi, Nov 01 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 (10,-9).

Crossrefs

Cf. A198965.

Programs

Magma

[(7*9^n-1)/2: n in [0..20]];

Mathematica

CoefficientList[Series[(3 + x)/(1 - 10 x + 9 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 03 2013 *)
LinearRecurrence[{10,-9},{3,31},30] (* Harvey P. Dale, Oct 10 2017 *)

PARI

a(n)=7*9^n\2 \\ Charles R Greathouse IV, Oct 16 2015

Formula

a(n) = 9*a(n-1)+4.

a(n) = 10*a(n-1)-9*a(n-2), n>1.

G.f.: (3 + x)/(1 - 10*x + 9*x^2). - Vincenzo Librandi, Jan 03 2013

From Elmo R. Oliveira, Aug 15 2024: (Start)

E.g.f.: exp(x)*(7*exp(8*x) - 1)/2.

a(n) = A198965(n)/2. (End)