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A302507 a(n) = 4*(3^n-1). 0
0, 8, 32, 104, 320, 968, 2912, 8744, 26240, 78728, 236192, 708584, 2125760, 6377288, 19131872, 57395624, 172186880, 516560648, 1549681952, 4649045864, 13947137600, 41841412808, 125524238432, 376572715304, 1129718145920, 3389154437768, 10167463313312 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Triameter of the n-Sierpinski carpet graph.
Binomial transform is 0,8,48,224,960,... A211012 shifted. - R. J. Mathar, Apr 07 2022
LINKS
Eric Weisstein's World of Mathematics, Graph Triameter
Eric Weisstein's World of Mathematics, Sierpinski Carpet Graph
FORMULA
a(n) = 4*A024023(n).
a(n) = 4*a(n-1) - 3*a(n-2).
G.f.: 8*x/((1 - x)*(1 - 3*x)).
a(n) = 8*A003462(n). - R. J. Mathar, Apr 07 2022
MATHEMATICA
Table[4 (3^n - 1), {n, 0, 20}]
4 (3^Range[0, 20] - 1)
LinearRecurrence[{4, -3}, {8, 32}, {0, 20}]
CoefficientList[Series[8 x/((1 - x) (1 - 3 x)), {x, 0, 20}], x]
PROG
(PARI) for(n=0, 30, print1(4*(3^n-1), ", ")) \\ G. C. Greubel, Apr 09 2018
(Magma) [4*(3^n -1): n in [0..30]]; // G. C. Greubel, Apr 09 2018
CROSSREFS
Cf. A024023.
Sequence in context: A178797 A357285 A100312 * A204643 A036393 A003201
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 09 2018
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)