A155660 a(n) = 9^n - 7^n + 1.

1, 3, 33, 387, 4161, 42243, 413793, 3959427, 37281921, 347066883, 3204309153, 29403732867, 268588249281, 2444976817923, 22198569382113, 201143570584707, 1819787258282241, 16444551185679363, 148466221699088673, 1339452822487618947, 12077873192759316801, 108860443267429075203

Offset: 0

Author

Mohammad K. Azarian, Jan 31 2009

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (17,-79,63).

Crossrefs

Cf. A155638, A155639, A155640, A155641, A155642, A155643, A155644, A155645, A155646, A155647, A155648, A155649, A155650, A155651, A155652, A155653, A155654, A155655, A155656, A155657, A155658, A155659.

Programs

Mathematica

LinearRecurrence[{17,-79,63},{1,3,33},30] (* Harvey P. Dale, Feb 25 2015 *)

PARI

a(n)=9^n-7^n+1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-9*x)-1/(1-7*x)+1/(1-x).

E.g.f.: exp(9*x)-exp(7*x)+exp(x).

a(n) = 16*a(n-1)-63*a(n-2)+48 with a(0) = 1, a(1) = 3. - Vincenzo Librandi, Jul 21 2010