A299277 Coordination sequence for "pcu-i" 3D uniform tiling.
1, 5, 13, 26, 46, 73, 104, 140, 187, 240, 292, 352, 417, 482, 567, 660, 740, 838, 944, 1031, 1150, 1290, 1399, 1531, 1677, 1787, 1944, 2130, 2261, 2431, 2624, 2750, 2941, 3180, 3334, 3538, 3777, 3920, 4149, 4440, 4610, 4852, 5144, 5297, 5560, 5910, 6097, 6373, 6717, 6881, 7182, 7590, 7787, 8101, 8504, 8672
Offset: 0
References
- B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #20.
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- V. A. Blatov, A. P. Shevchenko, D. M. Proserpio, Applied Topological Analysis of Crystal Structures with the Program Package ToposPro, Cryst. Growth Des. 2014, 14, 3576-3586.
- Reticular Chemistry Structure Resource (RCSR), The pcu-i tiling (or net)
- Index entries for linear recurrences with constant coefficients, signature (0,-1,1,0,1,2,0,2,-2,0,-2,-1,0,-1,1,0,1).
Crossrefs
See A299278 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
CoefficientList[Series[(x^16-x^15+x^14-2x^13+2x^12-x^11+4x^10+x^9+9x^8+12x^6-x^5+ 9x^4+4x^2+1)(x+1)^5/((1+x^2)(1-x^3)(1-x^6)^2),{x,0,60}],x] (* or *) LinearRecurrence[{ 2,-4,7,-10,14,-16,18,-18,16,-14,10,-7,4,-2,1},{1,5,13,26,46,73,104,140,187,240,292,352,417,482,567,660,740,838,944,1031},60] (* Harvey P. Dale, Mar 09 2024 *) -
PARI
Vec((x^16 - x^15 + x^14 - 2*x^13 + 2*x^12 - x^11 + 4*x^10 + x^9 + 9*x^8 + 12*x^6 - x^5 + 9*x^4 + 4*x^2 + 1) * (x + 1)^5 / ((1 + x^2)*(1 - x^3)*(1 - x^6)^2) + O(x^60)) \\ Colin Barker, Feb 14 2018
Formula
G.f.: (x^16 - x^15 + x^14 - 2*x^13 + 2*x^12 - x^11 + 4*x^10 + x^9 + 9*x^8 + 12*x^6 - x^5 + 9*x^4 + 4*x^2 + 1) * (x + 1)^5 / ((1 + x^2)*(1 - x^3)*(1 - x^6)^2). - N. J. A. Sloane, Feb 13 2018
a(n) = -a(n-2) + a(n-3) + a(n-5) + 2*a(n-6) + 2*a(n-8) - 2*a(n-9) - 2*a(n-11) - a(n-12) - a(n-14) + a(n-15) + a(n-17) for n>21. - Colin Barker, Feb 14 2018
Comments