A155645 a(n) = 7^n+6^n-1.

1, 12, 84, 558, 3696, 24582, 164304, 1103478, 7444416, 50431302, 342941424, 2340123798, 16018069536, 109949704422, 756587236944, 5217746494518, 36054040477056, 249557173431942, 1729973554578864, 12008254925383638

Offset: 0

Author

Mohammad K. Azarian, Jan 31 2009

Keywords

• nonn
• easy
• changed

Links

• Index entries for linear recurrences with constant coefficients, signature (14,-55,42).

Crossrefs

Cf. A155628, A155629, A155630, A155631, A155632, A155633, A155634, A155635, A155636, A155637, A155638, A155639, A155640, A155641, A155642, A155643, A155644.

Programs

Mathematica

Table[7^n+6^n-1,{n,0,20}] (* or *) LinearRecurrence[{14,-55,42},{1,12,84},20] (* Harvey P. Dale, May 08 2012 *)

PARI

a(n)=7^n+6^n-1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-7*x)+1/(1-6*x)-1/(1-x).

E.g.f.: e^(7*x)+e^(6*x)-e^x.

a(n) = 13*a(n-1)-42*a(n-2)-30 with a(0)=1, a(1)=12. - Vincenzo Librandi, Jul 21 2010

a(0)=1, a(1)=12, a(2)=84, a(n) = 14*a(n-1)-55*a(n-2)+42*a(n-3). - Harvey P. Dale, May 08 2012