OFFSET
0,2
COMMENTS
First 80 terms computed by Davide M. Proserpio using ToposPro.
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).
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
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 *)
PROG
(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
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.
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 10 2018
STATUS
approved