A221910 a(n) = 8^n + 8*n.
1, 16, 80, 536, 4128, 32808, 262192, 2097208, 16777280, 134217800, 1073741904, 8589934680, 68719476832, 549755813992, 4398046511216, 35184372088952, 281474976710784, 2251799813685384, 18014398509482128, 144115188075856024, 1152921504606847136, 9223372036854775976
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (10,-17,8).
Programs
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Magma
[8^n + 8*n: n in [0..30]];
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Magma
I:=[1, 16, 80]; [n le 3 select I[n] else 10*Self(n-1)-17*Self(n-2)+8*Self(n-3): n in [1..30]];
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Mathematica
Table[(8^n + 8 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 6 x - 63 x^2)/((1 - x)^2(1 - 8 x)), {x, 0, 30}], x] LinearRecurrence[{10,-17,8},{1,16,80},20] (* Harvey P. Dale, May 29 2021 *) -
PARI
a(n)=8^n+8*n \\ Charles R Greathouse IV, Apr 18 2013
Formula
G.f.: (1+6*x-63*x^2)/((1-x)^2*(1-8*x)).
a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3).
E.g.f.: exp(x)*(exp(7*x) + 8*x). - Elmo R. Oliveira, Sep 10 2024