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 A299281 Coordination sequence for "reo-e" 3D uniform tiling. 51
 1, 6, 19, 41, 72, 114, 166, 224, 288, 364, 454, 550, 648, 758, 886, 1020, 1152, 1296, 1462, 1634, 1800, 1978, 2182, 2392, 2592, 2804, 3046, 3294, 3528, 3774, 4054, 4340, 4608, 4888, 5206, 5530, 5832, 6146, 6502, 6864, 7200, 7548, 7942, 8342, 8712, 9094, 9526, 9964, 10368 (list; graph; refs; listen; history; text; internal format)
 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 #9. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Reticular Chemistry Structure Resource (RCSR), The reo-e tiling (or net) Index entries for linear recurrences with constant coefficients, signature (3,-5,7,-7,5,-3,1). FORMULA G.f.: (x+1)*(x^3+x^2+1)*(x^6-2*x^5+x^4+3*x^2+2*x+1) / ((x^2+1)^2*(1-x)^3). - N. J. A. Sloane, Feb 12 2018 a(n) = 3*a(n-1) - 5*a(n-2) + 7*a(n-3) - 7*a(n-4) + 5*a(n-5) - 3*a(n-6) + a(n-7) for n>8. - Colin Barker, Feb 14 2018 PROG (PARI) Vec((1 + x)*(1 + x^2 + x^3)*(1 + 2*x + 3*x^2 + x^4 - 2*x^5 + x^6) / ((1 - x)^3*(1 + x^2)^2) + O(x^60)) \\ Colin Barker, Feb 14 2018 CROSSREFS See A299282 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: A273571 A273778 A173980 * A212684 A035495 A061293 Adjacent sequences:  A299278 A299279 A299280 * A299282 A299283 A299284 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 10 2018 EXTENSIONS a(21)-a(40) from Davide M. Proserpio, Feb 12 2018 STATUS approved

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Last modified January 24 21:21 EST 2021. Contains 340411 sequences. (Running on oeis4.)