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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-17,8).

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

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 *)

Prog

(Magma) [8^n + 8*n: n in [0..30]]; /* or */ 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]];
(PARI) a(n)=8^n+8*n \\ Charles R Greathouse IV, Apr 18 2013

Crossrefs

Cf. A198398, A226201, A370661.

Sequence in context: A247817 A034570 A165963 * A069840 A000817 A192510

Adjacent sequences: A221907 A221908 A221909 * A221911 A221912 A221913

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 02 2013

Status

approved