A198398 a(n) = 8^n - 8n.

1, 0, 48, 488, 4064, 32728, 262096, 2097096, 16777152, 134217656, 1073741744, 8589934504, 68719476640, 549755813784, 4398046510992, 35184372088712, 281474976710528, 2251799813685112, 18014398509481840, 144115188075855720, 1152921504606846816, 9223372036854775640

Offset: 0

Author

Vincenzo Librandi, Oct 26 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-17,8).

Crossrefs

Cf. A005803, A107583, A107584, A107585.

Programs

Magma

[8^n-8*n: n in [0..25]];

Mathematica

CoefficientList[Series[(1 - 10*x + 65*x^2)/((1 - 8*x)*(1 -x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *)
LinearRecurrence[{10,-17,8},{1,0,48},30] (* Harvey P. Dale, Mar 13 2023 *)

PARI

a(n)=8^n-8*n \\ Charles R Greathouse IV, Jul 06 2017

Formula

a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3) for n > 2.

G.f.: (1 - 10*x + 65*x^2)/((1 - 8*x)*(1 -x)^2). - Vincenzo Librandi, Jan 04 2013

E.g.f.: exp(x)*(exp(7*x) - 8*x). - Elmo R. Oliveira, Sep 10 2024