OFFSET
0,2
COMMENTS
First 20 terms computed byDavide 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
FromColin 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
SeeA299286 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 inA299266 for overview.
Cf.A056594.
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 10 2018
STATUS
approved