A048491 a(n) = T(8,n), array T given by A048483.

1, 10, 28, 64, 136, 280, 568, 1144, 2296, 4600, 9208, 18424, 36856, 73720, 147448, 294904, 589816, 1179640, 2359288, 4718584, 9437176, 18874360, 37748728, 75497464, 150994936, 301989880, 603979768, 1207959544, 2415919096

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

n-th difference of a(n), a(n-1), ..., a(0) is (9, 9, 9, ...).

Links

• Index entries for linear recurrences with constant coefficients, signature (3, -2).

Programs

Mathematica

a=1; lst={a}; k=9; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 16 2008 *)
9*2^Range[0,30]-8 (* Harvey P. Dale, May 14 2021 *)

Formula

a(n) = 9 * 2^n - 8. - Ralf Stephan

Equals binomial transform of [1, 9, 9, 9, ...]. - Gary W. Adamson, Apr 29 2008

a(n) = 2*a(n-1) + 8, with a(0)=1. - Vincenzo Librandi, Aug 06 2010

a(n) = 2*A053209(n), n>0. - Philippe Deléham, Apr 15 2013

a(n) = 3*a(n-1) - 2*a(n-2) with a(0)=1, a(1)=10. - Philippe Deléham, Apr 15 2013

G.f.: (1+7*x)/((1-x)*(1-2*x)). - Philippe Deléham, Apr 15 2013