A155647 a(n) = 9^n+6^n-1^n.

1, 14, 116, 944, 7856, 66824, 578096, 5062904, 44726336, 397498184, 3547250576, 31743856664, 284606318816, 2554926522344, 22955156619056, 206361317079224, 1855841298759296, 16694108359111304, 150196195253667536

Offset: 0

Author

Mohammad K. Azarian, Jan 31 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (16,-69,54).

Crossrefs

Cf. A155628, A155629, A155630, A155631, A155632, A155633, A155634, A155635, A155636, A155637, A155638, A155639, A155640, A155641, A155642, A155643, A155644, A155645, A155646.

Programs

Mathematica

Table[9^n+6^n-1,{n,0,30}] (* or *) LinearRecurrence[{16,-69,54},{1,14,116},30] (* Harvey P. Dale, Dec 04 2012 *)

PARI

a(n)=9^n+6^n-1 \\ Charles R Greathouse IV, Sep 24 2015

Formula

G.f.: 1/(1-9*x)+1/(1-6*x)-1/(1-x). E.g.f.: e^(9*x)+e^(6*x)-e^x.

a(n) = 15*a(n-1)-54*a(n-2)-40 with a(0)=1, a(1)=14. - Vincenzo Librandi, Jul 21 2010

a(0)=1, a(1)=14, a(2)=116, a(n) = 16*a(n-1)-69*a(n-2)+54*a(n-3). - Harvey P. Dale, Dec 04 2012