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A299279
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Coordination sequence for "reo" 3D uniform tiling.
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51
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1, 8, 30, 68, 126, 180, 286, 348, 510, 572, 798, 852, 1150, 1188, 1566, 1580, 2046, 2028, 2590, 2532, 3198, 3092, 3870, 3708, 4606, 4380, 5406, 5108, 6270, 5892, 7198, 6732, 8190, 7628, 9246, 8580, 10366, 9588, 11550, 10652, 12798, 11772, 14110, 12948, 15486, 14180
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refs;
listen;
history;
text;
internal format)
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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 #7.
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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 tiling (or net)
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
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FORMULA
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G.f.: (4*x^7 - 3*x^6 + 39*x^4 + 44*x^3 + 27*x^2 + 8*x + 1) / (1 - x^2)^3.
From Colin Barker, Feb 11 2018: (Start)
a(n) = 8*n^2 - 2 for n>1.
a(n) = 7*n^2 + 5 for n>1.
a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>7.
(End)
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PROG
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(PARI) Vec((1 + 8*x + 27*x^2 + 44*x^3 + 39*x^4 - 3*x^6 + 4*x^7) / ((1 - x)^3*(1 + x)^3) + O(x^60)) \\ Colin Barker, Feb 11 2018
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CROSSREFS
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See A299280 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: A074670 A092277 A008469 * A184323 A004639 A317637
Adjacent sequences: A299276 A299277 A299278 * A299280 A299281 A299282
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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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STATUS
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approved
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