A010001 a(0) = 1, a(n) = 5*n^2 + 2 for n>0.
1, 7, 22, 47, 82, 127, 182, 247, 322, 407, 502, 607, 722, 847, 982, 1127, 1282, 1447, 1622, 1807, 2002, 2207, 2422, 2647, 2882, 3127, 3382, 3647, 3922, 4207, 4502, 4807, 5122, 5447, 5782, 6127, 6482, 6847, 7222, 7607, 8002, 8407, 8822, 9247, 9682, 10127, 10582
Offset: 0
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).
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.
Programs
-
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 *) -
PARI
A010001(n)=5*n^2+2-!n \\ M. F. Hasler, Feb 14 2012
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
Extensions
More terms from Bruno Berselli, Feb 06 2012
Comments