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A299287
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Coordination sequence for "tcd" 3D uniform tiling.
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51
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1, 10, 33, 72, 126, 196, 281, 382, 498, 630, 777, 940, 1118, 1312, 1521, 1746, 1986, 2242, 2513, 2800, 3102, 3420, 3753, 4102, 4466, 4846, 5241, 5652, 6078, 6520, 6977, 7450, 7938, 8442, 8961, 9496, 10046, 10612, 11193, 11790, 12402, 13030, 13673, 14332
(list;
graph;
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 #3.
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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 tcd tiling (or net)
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
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FORMULA
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G.f.: (x^4 + 8*x^3 + 13*x^2 + 8*x + 1) / ((1 + x)*(1 - x)^3).
From Colin Barker, Feb 11 2018: (Start)
a(n) = (31*n^2 + 8) / 4 for even n>0.
a(n) = (31*n^2 + 9) / 4 for odd n>0.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.
(End)
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PROG
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(PARI) Vec((1 + 8*x + 13*x^2 + 8*x^3 + x^4) / ((1 - x)^3*(1 + x)) + O(x^60)) \\ Colin Barker, Feb 11 2018
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CROSSREFS
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See A299288 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: A348427 A063160 A065149 * A299285 A081437 A085490
Adjacent sequences: A299284 A299285 A299286 * A299288 A299289 A299290
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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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