|
|
A008137
|
|
Coordination sequence T1 for Zeolite Code LTA and RHO.
|
|
71
|
|
|
1, 4, 9, 17, 28, 42, 60, 81, 105, 132, 162, 196, 233, 273, 316, 362, 412, 465, 521, 580, 642, 708, 777, 849, 924, 1002, 1084, 1169, 1257, 1348, 1442, 1540, 1641, 1745, 1852, 1962, 2076, 2193, 2313, 2436, 2562, 2692, 2825, 2961, 3100, 3242, 3388, 3537, 3689
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Also, growth series for the affine Coxeter (or Weyl) groups B_3. - N. J. A. Sloane, Jan 11 2016
Also, coordination sequence for "rho" 3D uniform tiling. - N. J. A. Sloane, Feb 10 2018
|
|
REFERENCES
|
N. Bourbaki, Groupes et Algèbres de Lie, Chap. 4, 5 and 6, Hermann, Paris, 1968. See Chap. VI, Section 4, Problem 10b, page 231, W_a(t).
B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tilings #25 and 27.
W. M. Meier, D. H. Olson and Ch. Baerlocher, Atlas of Zeolite Structure Types, 4th Ed., Elsevier, 1996.
|
|
LINKS
|
|
|
FORMULA
|
a(5*m+k) = 40*m^2 + 16*k*m + one of 5 numbers depending on k, 0 <= k < 5 (N. J. A. Sloane).
G.f.: (1-x^2)*(1-x^4)*(1-x^6)/((1-x)^4*(1-x^3)*(1-x^5)). This can also be written as (x+1)^3*(x^2+1)*(x^2-x+1)/((1-x)^3*(x^4+x^3+x^2+x+1)). - N. J. A. Sloane, Feb 10 2018
a(n) = 12/5 - 0^n + (8/5)*n^2 - (1/25)*(5+sqrt(5))*cos(2*Pi*n/5) - (1/25)*(5-sqrt(5))*cos(4*Pi*n/5). - Eric Simon Jacob, Feb 12 2023
|
|
MAPLE
|
(1-x^2)*(1-x^4)*(1-x^6)/((1-x)^4*(1-x^3)*(1-x^5));
seq(coeff(series(%, x, n+1), x, n), n=0..48);
|
|
CROSSREFS
|
The 28 uniform 3D tilings: cab: A299266, A299267; crs: A299268, A299269; fcu: A005901, A005902; fee: A299259, A299265; flu-e: A299272, A299273; fst: A299258, A299264; hal: A299274, A299275; hcp: A007899, A007202; hex: A005897, A005898; kag: A299256, A299262; lta: A008137, A299276; pcu: A005899, A001845; pcu-i: A299277, A299278; reo: A299279, A299280; reo-e: A299281, A299282; rho: A008137, A299276; sod: A005893, A005894; sve: A299255, A299261; svh: A299283, A299284; svj: A299254, A299260; svk: A010001, A063489; tca: A299285, A299286; tcd: A299287, A299288; tfs: A005899, A001845; tsi: A299289, A299290; ttw: A299257, A299263; ubt: A299291, A299292; bnn: A007899, A007202. See the Proserpio link in A299266 for overview.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|