A155659 a(n) = 8^n - 7^n + 1.

1, 2, 16, 170, 1696, 15962, 144496, 1273610, 11012416, 93864122, 791266576, 6612607850, 54878189536, 452866803482, 3719823438256, 30436810578890, 248242046141056, 2019169299698042, 16385984911571536, 132716292890482730, 1073129238309234976, 8664826172771491802

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 (16,-71,56).

Crossrefs

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

Programs

Mathematica

Table[8^n - 7^n + 1, {n, 0, 25}] (* Paolo Xausa, Aug 03 2024 *)

PARI

a(n)=8^n-7^n+1 \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-8*x)-1/(1-7*x)+1/(1-x).

E.g.f.: exp(8*x)-exp(7*x)+exp(x).

a(n) = 15*a(n-1)-56*a(n-2)+42 with a(0) = 1, a(1) = 2. - Vincenzo Librandi, Jul 21 2010