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A299268
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Coordination sequence for "crs" 3D uniform tiling formed from tetrahedra and truncated tetrahedra.
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51
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1, 6, 18, 48, 78, 126, 182, 240, 330, 390, 522, 576, 758, 798, 1038, 1056, 1362, 1350, 1730, 1680, 2142, 2046, 2598, 2448, 3098, 2886, 3642, 3360, 4230, 3870, 4862, 4416, 5538, 4998, 6258, 5616, 7022, 6270, 7830, 6960, 8682, 7686, 9578, 8448, 10518, 9246
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history;
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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 #6.
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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 crs 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.: (x^6 + 27*x^4 + 30*x^3 + 15*x^2 + 6*x + 1) / (1 - x^2)^3.
From Colin Barker, Feb 09 2018: (Start)
a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>6.
a(n) = (11*n^2 - 6*n + 4) / 2 for n>0 and even.
a(n) = 3 * (3*n^2 + 2*n - 1) / 2 for n odd.
(End)
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MATHEMATICA
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CoefficientList[Series[(x^6+27*x^4+30*x^3+15*x^2+6*x+1)/(1-x^2)^3, {x, 0, 50}], x] (* G. C. Greubel, Feb 20 2018 *)
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PROG
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(PARI) Vec((1 + 6*x + 15*x^2 + 30*x^3 + 27*x^4 + x^6) / ((1 - x)^3*(1 + x)^3) + O(x^60)) \\ Colin Barker, Feb 09 2018
(Magma) I:=[18, 48, 78, 126, 182, 240, 330]; [1, 6] cat [n le 6 select I[n] else 3*Self(n-2) -3*Self(n-4) + Self(n-6): n in [1..30]]; // G. C. Greubel, Feb 20 2018
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CROSSREFS
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See A299269 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: A261016 A328890 A188379 * A248462 A256010 A128543
Adjacent sequences: A299265 A299266 A299267 * A299269 A299270 A299271
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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 07 2018
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STATUS
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approved
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