A156198 a(n) = 2*a(n-1)+3 with n>1, a(1)=8.

8, 19, 41, 85, 173, 349, 701, 1405, 2813, 5629, 11261, 22525, 45053, 90109, 180221, 360445, 720893, 1441789, 2883581, 5767165, 11534333, 23068669, 46137341, 92274685, 184549373, 369098749, 738197501, 1476395005, 2952790013

Offset: 1

Author

Vincenzo Librandi, Feb 08 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Programs

Magma

I:=[8, 19]; [n le 2 select I[n] else 3*Self(n-1)-2*Self(n-2): n in [1..30]]; // Librandi Vincenzo, May 02 2012

Mathematica

LinearRecurrence[{3,-2},{8,19},30] (* Vincenzo Librandi, May 02 2012 *)
NestList[2#+3&,8,30] (* Harvey P. Dale, Oct 17 2016 *)

Formula

G.f.: (8*x-5*x^2)/(1-3*x+2*x^2). [Philippe Deléham, Feb 09 2009]

a(n) = 3*a(n-1)-2*a(n-2) = 11*2^(n-1)-3. [R. J. Mathar, Feb 19 2009]