A221906 a(n) = 4^n + 4*n.

1, 8, 24, 76, 272, 1044, 4120, 16412, 65568, 262180, 1048616, 4194348, 16777264, 67108916, 268435512, 1073741884, 4294967360, 17179869252, 68719476808, 274877907020, 1099511627856, 4398046511188

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Formula

G.f.: (1 + 2*x - 15*x^2)/((1-x)^2*(1-4*x)).

a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3).

Mathematica

Table[(4^n + 4 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 2 x - 15 x^2)/((1 - x)^2 (1 - 4 x)), {x, 0, 30}], x]

Prog

(Magma) [4^n + 4*n: n in [0..30]]; /* or */ I:=[1, 8, 24]; [n le 3 select I[n] else 6*Self(n-1)-9*Self(n-2)+4*Self(n-3): n in [1..30]];

Crossrefs

Cf. A107584, A370659.

Sequence in context: A005051 A303402 A078158 * A116486 A179609 A241690

Adjacent sequences: A221903 A221904 A221905 * A221907 A221908 A221909

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 02 2013

Status

approved