A024089 a(n) = 8^n - n.
1, 7, 62, 509, 4092, 32763, 262138, 2097145, 16777208, 134217719, 1073741814, 8589934581, 68719476724, 549755813875, 4398046511090, 35184372088817, 281474976710640, 2251799813685231, 18014398509481966, 144115188075855853, 1152921504606846956, 9223372036854775787
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..400
- Index entries for linear recurrences with constant coefficients, signature (10,-17,8).
Crossrefs
Programs
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Magma
[8^n-n: n in [0..20]]; // Vincenzo Librandi, Jul 05 2011
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Magma
I:=[1,7,62]; [n le 3 select I[n] else 10*Self(n-1)-17*Self(n-2)+8*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 17 2013
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Mathematica
Table[8^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 9 x^2) / ((1 - 8 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 17 2013 *) LinearRecurrence[{10,-17,8},{1,7,62},30] (* Harvey P. Dale, Sep 28 2017 *) -
PARI
a(n)=8^n-n \\ Charles R Greathouse IV, Oct 07 2015
Formula
From Vincenzo Librandi, Jun 17 2013: (Start)
G.f.: (1-3*x+9*x^2)/((1-8*x)*(1-x)^2).
a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3). (End)
E.g.f.: exp(x)*(exp(7*x) - x). - Elmo R. Oliveira, Sep 10 2024