OFFSET
0,2
COMMENTS
Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3^3.4^2 2D tiling (cf. A008706). - N. J. A. Sloane, Feb 07 2018
REFERENCES
B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #13.
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Reticular Chemistry Structure Resource (RCSR), The svk tiling (or net)
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (1+x)*(1+3*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 06 2012
E.g.f.: (x*(x+1)*5+2)*e^x-1. - Gopinath A. R., Feb 14 2012
Sum_{n>=0} 1/a(n) = 3/4+sqrt(10)/20*Pi*coth( Pi/5 *sqrt 10) = 1.2657655... - R. J. Mathar, May 07 2024
MATHEMATICA
lst={}; Do[AppendTo[lst, 5*n^2+2], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 15 2009 *)
Join[{1}, 5 Range[46]^2 + 2] (* Bruno Berselli, Feb 06 2012 *)
PROG
(PARI) A010001(n)=5*n^2+2-!n \\ M. F. Hasler, Feb 14 2012
CROSSREFS
See A063489 for partial sums.
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
EXTENSIONS
More terms from Bruno Berselli, Feb 06 2012
STATUS
approved