OFFSET
0,2
COMMENTS
First 20 terms computed by Davide M. Proserpio using ToposPro.
LINKS
B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #4.
Reticular Chemistry Structure Resource (RCSR), The tea tiling (or net)
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).
FORMULA
From Colin Barker, Feb 11 2018: (Start)
G.f.: (1 + 8*x + 14*x^2 + 17*x^3 + 14*x^4 + 8*x^5 + x^6) / ((1 - x)^3*(1 + x)*(1 + x^2)).
a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) for n>6. (End)
[I suspect Barker's formulas only conjectures. - N. J. A. Sloane, Jun 12 2024]
If the above formulas are true, then a(n) = (31 - 3*(-1)^n + 126*n^2 + 4*A056594(n))/16 for n > 0. - Stefano Spezia, Jun 08 2024
MATHEMATICA
LinearRecurrence[{2, -1, 0, 1, -2, 1}, {1, 10, 33, 73, 128, 199, 285}, 50] (* Harvey P. Dale, May 09 2022 *)
PROG
(PARI) a(n)=([0, 1, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; 1, -2, 1, 0, -1, 2]^n*[1; 10; 33; 73; 128; 199])[1, 1] \\ Charles R Greathouse IV, Oct 18 2022
CROSSREFS
See A299286 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.
Cf. A056594.
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 10 2018
STATUS
approved