A155605 7^n+3^n-1.

1, 9, 57, 369, 2481, 17049, 118377, 825729, 5771361, 40373289, 282534297, 1977503889, 13841818641, 96890604729, 678227855817, 4747575858849, 33232973616321, 232630643127369, 1628413985330937, 11398896347634609

Offset: 0

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-31,21).

Crossrefs

Cf. A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604.

Programs

Mathematica

Table[7^n+3^n-1,{n,0,20}] (* or *) LinearRecurrence[{11,-31,21},{1,9,57},20] (* Harvey P. Dale, Nov 09 2012 *)

PARI

a(n)=7^n+3^n-1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-7*x)+1/(1-3*x)-1/(1-x). E.g.f.: e^(7*x)+e^(3*x)-e^x.

a(n)=10*a(n-1)-21*a(n-2)-12 with a(0)=1, a(1)=9 - Vincenzo Librandi, Jul 21 2010

a(0)=1, a(1)=9, a(2)=57, a(n)=11*a(n-1)-31*a(n-2)+21*a(n-3). - Harvey P. Dale, Nov 09 2012