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 A299268 Coordination sequence for "crs" 3D uniform tiling formed from tetrahedra and truncated tetrahedra. 51
 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 (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 #6. LINKS 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). FORMULA 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) MATHEMATICA 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 *) PROG (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 CROSSREFS 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: A304161 A261016 A188379 * A248462 A256010 A128543 Adjacent sequences:  A299265 A299266 A299267 * A299269 A299270 A299271 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 07 2018 STATUS approved

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Last modified December 17 06:45 EST 2018. Contains 318192 sequences. (Running on oeis4.)