A299289 Coordination sequence for "tsi" 3D uniform tiling.

1, 8, 28, 60, 106, 164, 236, 320, 418, 528, 652, 788, 938, 1100, 1276, 1464, 1666, 1880, 2108, 2348, 2602, 2868, 3148, 3440, 3746, 4064, 4396, 4740, 5098, 5468, 5852, 6248, 6658, 7080, 7516, 7964, 8426, 8900, 9388, 9888, 10402, 10928

Offset

0,2

Comments

First 20 terms computed by Davide M. Proserpio using ToposPro.

References

B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #12.

Links

Table of n, a(n) for n=0..41.

Reticular Chemistry Structure Resource (RCSR), The tsi tiling (or net)

Formula

Conjectures from Colin Barker, Feb 11 2018: (Start)

G.f.: (1 + 6*x + 12*x^2 + 6*x^3 + x^4) / ((1 - x)^3*(1 + x)).

a(n) = (13*n^2 + 4) / 2 for n>0 and even.

a(n) = (13*n^2 + 3) / 2 for n odd.

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.

(End)

Crossrefs

See A299290 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.

Sequence in context: A045850 A264354 A033580 * A212515 A342251 A007331

Adjacent sequences: A299286 A299287 A299288 * A299290 A299291 A299292

Keyword

nonn

Author

N. J. A. Sloane, Feb 10 2018

Status

approved