A299279 Coordination sequence for "reo" 3D uniform tiling.
1, 8, 30, 68, 126, 180, 286, 348, 510, 572, 798, 852, 1150, 1188, 1566, 1580, 2046, 2028, 2590, 2532, 3198, 3092, 3870, 3708, 4606, 4380, 5406, 5108, 6270, 5892, 7198, 6732, 8190, 7628, 9246, 8580, 10366, 9588, 11550, 10652, 12798, 11772, 14110, 12948, 15486, 14180
Offset: 0
References
- B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #7.
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Reticular Chemistry Structure Resource (RCSR), The reo tiling (or net)
- Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
Crossrefs
See A299280 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
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Mathematica
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {1, 8, 30, 68, 126, 180, 286, 348}, 50] (* Paolo Xausa, Jan 16 2025 *) -
PARI
Vec((1 + 8*x + 27*x^2 + 44*x^3 + 39*x^4 - 3*x^6 + 4*x^7) / ((1 - x)^3*(1 + x)^3) + O(x^60)) \\ Colin Barker, Feb 11 2018
Formula
G.f.: (4*x^7 - 3*x^6 + 39*x^4 + 44*x^3 + 27*x^2 + 8*x + 1) / (1 - x^2)^3.
From Colin Barker, Feb 11 2018: (Start)
a(n) = 8*n^2 - 2 for even n > 1.
a(n) = 7*n^2 + 5 for odd n > 1.
a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>7. (End)
E.g.f.: 3 - 4*x + (8*x^2 + 7*x - 2)*cosh(x) + (7*x^2 + 8*x + 5)*sinh(x). - Stefano Spezia, Jun 06 2024
Comments