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A299281
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Coordination sequence for "reo-e" 3D uniform tiling.
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51
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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
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OFFSET
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0,2
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COMMENTS
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First 20 terms computed by Davide M. Proserpio using ToposPro.
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REFERENCES
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B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #9.
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LINKS
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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).
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FORMULA
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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
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Feb 10 2018
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EXTENSIONS
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a(21)-a(40) from Davide M. Proserpio, Feb 12 2018
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STATUS
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approved
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