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 A299291 Coordination sequence for "ubt" 3D uniform tiling. 51
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First 80 terms computed by Davide M. Proserpio using ToposPro. 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). 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 PROG (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 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. Sequence in context: A256666 A319007 A211651 * A019262 A212919 A280230 Adjacent sequences:  A299288 A299289 A299290 * A299292 A299293 A299294 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 10 2018 STATUS approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)