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%I #19 Aug 20 2021 12:06:08
%S 1,5,14,29,56,85,130,181,226,299,382,445,538,635,708,845,962,1079,
%T 1218,1363,1456,1671,1808,1987,2170,2365,2470,2777,2920,3169,3394,
%U 3641,3750,4163,4298,4625,4890,5191,5296,5829,5942,6355,6658,7015,7108,7775,7852,8359,8698,9113,9186
%N Coordination sequence for "ubt" 3D uniform tiling.
%C First 80 terms computed by _Davide M. Proserpio_ using ToposPro.
%D B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #10.
%H Colin Barker, <a href="/A299291/b299291.txt">Table of n, a(n) for n = 0..1000</a>
%H Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/nets/ubt">The ubt tiling (or net)</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (-1,0,1,1,0,2,2,0,-2,-2,0,-1,-1,0,1,1).
%F 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
%F 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
%t 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 *)
%o (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
%Y See A299292 for partial sums.
%Y 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.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Feb 10 2018
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