A155597 a(n) = 6^n - 2^n + 1.

1, 5, 33, 209, 1281, 7745, 46593, 279809, 1679361, 10077185, 60465153, 362795009, 2176778241, 13060685825, 78364147713, 470184951809, 2821109841921, 16926659313665, 101559956406273, 609359739486209, 3656158439014401, 21936950638280705, 131621703838072833

Offset: 0

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-20,12).

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596.

Programs

Mathematica

Table[6^n-2^n+1,{n,0,20}] (* or *) LinearRecurrence[{9,-20,12},{1,5,33},20] (* Harvey P. Dale, Jul 13 2011 *)

PARI

a(n) = 6^n-2^n+1 \\ Charles R Greathouse IV, Jul 25 2011

Formula

G.f.: 1/(1-6*x)-1/(1-2*x)+1/(1-x).

E.g.f.: exp(6*x)-exp(2*x)+exp(x).

a(n) = 8*a(n-1)-12*a(n-2)+5 with a(0)=1, a(1)=5. - Vincenzo Librandi, Jul 21 2010

a(0)=1, a(1)=5, a(2)=33, a(n) = 9*a(n-1)-20*a(n-2)+12*a(n-3). - Harvey P. Dale, Jul 13 2011

a(n) = A248216(n)+1. - R. J. Mathar, Mar 10 2022