A302507 a(n) = 4*(3^n-1).

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

Offset: 0

Author

Eric W. Weisstein, Apr 09 2018

Keywords

• nonn
• easy

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
• Index entries for linear recurrences with constant coefficients, signature (4,-3).

Crossrefs

Cf. A024023.

Programs

Magma

[4*(3^n -1): n in [0..30]]; // G. C. Greubel, Apr 09 2018

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]

PARI

for(n=0,30, print1(4*(3^n-1), ", ")) \\ G. C. Greubel, Apr 09 2018

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