A291938 a(n) = 2^(n - 1) (n - mod(n, 2)).

0, 4, 8, 32, 64, 192, 384, 1024, 2048, 5120, 10240, 24576, 49152, 114688, 229376, 524288, 1048576, 2359296, 4718592, 10485760, 20971520, 46137344, 92274688, 201326592, 402653184, 872415232, 1744830464, 3758096384, 7516192768, 16106127360

Offset

1,2

Comments

Agrees with independence number of the n-cube connected cycle graph for at least 3 <= n <= 8.

Links

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, Cube-Connected Cycle Graph.

Eric Weisstein's World of Mathematics, Independence Number.

Index entries for linear recurrences with constant coefficients, signature (2,4,-8).

Formula

a(n) = 2^(n - 1) (n - mod(n, 2)).

a(n) = 2*a(n-1) + 4*a(n-2) - 8*a(n-3).

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

a(n) = 2^n*A004526(n). - R. J. Mathar, Mar 08 2021

Sum_{n>=2} 1/a(n) = (3/2)*log(4/3). - Amiram Eldar, Apr 22 2022

Mathematica

Table[2^(n - 1) (n - Mod[n, 2]), {n, 20}]
LinearRecurrence[{2, 4, -8}, {0, 4, 8}, 20]
CoefficientList[Series[(4 x)/((1 - 2 x)^2 (1 + 2 x)), {x, 0, 20}], x]

Crossrefs

Cf. A004526.

Sequence in context: A050442 A229953 A331408 * A358046 A094015 A094867

Adjacent sequences: A291935 A291936 A291937 * A291939 A291940 A291941

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 06 2017

Status

approved