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A291938
a(n) = 2^(n - 1) (n - mod(n, 2)).
0
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
Eric Weisstein's World of Mathematics, Cube-Connected Cycle Graph.
Eric Weisstein's World of Mathematics, Independence Number.
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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 06 2017
STATUS
approved