A102485 a(n) = 5*3^n - 4*2^n.

1, 7, 29, 103, 341, 1087, 3389, 10423, 31781, 96367, 291149, 877543, 2640821, 7938847, 23849309, 71613463, 214971461, 645176527, 1936053869, 5809210183, 17429727701, 52293377407, 156888520829, 470682339703, 1412080573541, 4236308829487, 12709060706189

Offset: 0

Author

N. J. A. Sloane, Feb 25 2005

Keywords

• nonn
• easy

References

• B. M. E. Moret and H. D. Shapiro, Algorithms from P to NP, Benjamin/Cummings, Vol. 1, 1991; p. 63.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-6).

Programs

Magma

I:=[1, 7]; [n le 2 select I[n] else 5*Self(n-1)-6*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jan 15 2012

Maple

a := proc(n) option remember; if n = 0 then RETURN(1) end if; if n = 1 then RETURN(7) end if; 5*a(n - 1) - 6*a(n - 2); end proc;

Mathematica

LinearRecurrence[{5,-6},{1,7},30] (* Vincenzo Librandi, Jan 15 2012 *)
Table[5*3^n-4*2^n,{n,0,30}] (* Harvey P. Dale, Jul 16 2024 *)

PARI

a(n)=5*3^n-4<Charles R Greathouse IV, Jan 15 2012

Formula

a(n) = 5*a(n - 1) - 6*a(n - 2).

G.f.: (1+2*x)/((1-2*x)*(1-3*x)). - Colin Barker, Jan 14 2012

a(n) = A217764(n,8). - Ross La Haye, Mar 27 2013

a(n) = A001047(n+1)+2*A001047(n). - R. J. Mathar, May 14 2024

Extensions

New definition from Ralf Stephan, May 17 2007