|
|
A365608
|
|
Number of degree 4 vertices in the n-Sierpinski carpet graph.
|
|
9
|
|
|
0, 4, 100, 1060, 9316, 77092, 624484, 5019172, 40223332, 321996580, 2576602468, 20614709284, 164923342948, 1319403749668, 10555281015652, 84442401180196, 675539668606564, 5404318726347556, 43234553943265636, 345876443943580708, 2767011588741012580, 22136092821505201444, 177088742906772914020
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
The level 0 Sierpinski carpet graph is a single vertex. The level n Sierpinski carpet graph is formed from 8 copies of level n-1 by joining boundary vertices between adjacent copies.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (3/10)*8^n - (32/15)*3^n + 4.
a(n) = 8*a(n-1) + 32*3^(n-2) - 28.
G.f.: 4*x^2*(1 + 13*x)/((1 - x)*(1 - 3*x)*(1 - 8*x)). - Stefano Spezia, Sep 12 2023
|
|
EXAMPLE
|
The level 1 Sierpinski carpet graph is an 8-cycle, which has 8 degree 2 vertices and 0 degree 3 or 4 vertices. Thus a(1) = 0.
|
|
MATHEMATICA
|
LinearRecurrence[{12, -35, 24}, {0, 4, 100}, 30] (* Paolo Xausa, Oct 16 2023 *)
|
|
PROG
|
(Python)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|