A299291 Coordination sequence for "ubt" 3D uniform tiling.
1, 5, 14, 29, 56, 85, 130, 181, 226, 299, 382, 445, 538, 635, 708, 845, 962, 1079, 1218, 1363, 1456, 1671, 1808, 1987, 2170, 2365, 2470, 2777, 2920, 3169, 3394, 3641, 3750, 4163, 4298, 4625, 4890, 5191, 5296, 5829, 5942, 6355, 6658, 7015, 7108, 7775, 7852, 8359, 8698, 9113, 9186
Offset: 0
References
- B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #10.
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Reticular Chemistry Structure Resource (RCSR), The ubt tiling (or net)
- Index entries for linear recurrences with constant coefficients, signature (-1,0,1,1,0,2,2,0,-2,-2,0,-1,-1,0,1,1).
Crossrefs
See A299292 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[{-1,0,1,1,0,2,2,0,-2,-2,0,-1,-1,0,1,1},{1,5,14,29,56,85,130,181,226,299,382,445,538,635,708,845,962,1079,1218,1363,1456},60] (* Harvey P. Dale, Aug 20 2021 *) -
PARI
Vec((12*x^20 + 16*x^19 - 20*x^17 - 27*x^16 - 8*x^15 + 3*x^14 + 46*x^13 + 115*x^12 + 176*x^11 + 212*x^10 + 226*x^9 + 228*x^8 + 214*x^7 + 170*x^6 + 122*x^5 + 79*x^4 + 42*x^3 + 19*x^2 + 6*x + 1) / ((1 + x)*(1 - x^3)*(1 - x^6)^2) + O(x^50)) \\ Colin Barker, Feb 14 2018
Formula
G.f.: (12*x^20 + 16*x^19 - 20*x^17 - 27*x^16 - 8*x^15 + 3*x^14 + 46*x^13 + 115*x^12 + 176*x^11 + 212*x^10 + 226*x^9 + 228*x^8 + 214*x^7 + 170*x^6 + 122*x^5 + 79*x^4 + 42*x^3 + 19*x^2 + 6*x + 1) / ((1 + x)*(1 - x^3)*(1 - x^6)^2). - N. J. A. Sloane, Feb 13 2018
a(n) = -a(n-1) + a(n-3) + a(n-4) + 2*a(n-6) + 2*a(n-7) - 2*a(n-9) - 2*a(n-10) - a(n-12) - a(n-13) + a(n-15) + a(n-16) for n>17. - Colin Barker, Feb 14 2018
Comments