A155599 a(n) = 8^n - 2^n + 1^n.

1, 7, 61, 505, 4081, 32737, 262081, 2097025, 16776961, 134217217, 1073740801, 8589932545, 68719472641, 549755805697, 4398046494721, 35184372056065, 281474976645121, 2251799813554177, 18014398509219841, 144115188075331585

Offset: 0

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (11,-26,16).

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598.

Programs

Mathematica

Table[8^n-2^n+1,{n,0,30}] (* or *) LinearRecurrence[{11,-26,16},{1,7,61},30] (* Harvey P. Dale, Feb 25 2014 *)

PARI

a(n)=8^n-2^n+1 \\ Charles R Greathouse IV, Sep 24 2015

Formula

G.f.: 1/(1-8*x) - 1/(1-2*x) + 1/(1-x).

E.g.f.: e^(8*x) - e^(2*x) + e^x.

a(n) = 10*a(n-1) - 16*a(n-2) + 7 with a(0)=1, a(1)=7 - Vincenzo Librandi, Jul 21 2010

a(n) = A248217(n)+1. - R. J. Mathar, Mar 10 2022