|
Search: id:A097108
|
|
|
| A097108 |
|
If a geodesic dome is made by dividing each triangle of an icosahedron into n^2 identical equilateral triangles and the vertices of those newly created triangles are pushed out from the center to lie on the surface of the sphere in which the icosahedron is inscribed, then this sequence gives the number of different strut lengths that are required to build the dome. |
|
+0
1
|
|
| 1, 2, 3, 6, 9, 9, 16, 20, 18, 30, 36, 30, 49, 56, 45, 72, 81, 63, 100, 110, 84, 132, 144, 108, 169, 182, 135, 210, 225, 165, 256, 272, 198, 306, 324, 234, 361, 380, 273, 420, 441, 315, 484, 506, 360, 552, 576, 408, 625, 650, 459, 702, 729, 513, 784, 812, 570, 870
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
Tara Landry, Desert Domes.
|
|
FORMULA
|
Satisfies a linear recurrence with characteristic polynomial (1+x^3)(1-x^3)^3.
|
|
EXAMPLE
|
a(4) = 6 since we can build a "4V" dome of radius 1 using 30 struts of length .25318, 30 struts of length .29453, 70 of length .31287, 30 of length .32492 and 30 of length .29859. The number 6 indicates the number of different jig settings we'd have to use to manufacture all the struts for this dome.
|
|
CROSSREFS
|
Sequence in context: A088329 A087494 A021426 this_sequence A094351 A061910 A007086
Adjacent sequences: A097105 A097106 A097107 this_sequence A097109 A097110 A097111
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Tom Davis (tomrdavis(AT)earthlink.net), Sep 15 2004
|
|
|
Search completed in 0.002 seconds
|
