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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
Reticular Chemistry Structure Resource (RCSR), The crs tiling (or net)
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)
E.g.f.: ((11*x^2 + 15*x + 4)*cosh(x) + (9*x^2 + 5*x - 3)*sinh(x) - 2)/2. - Stefano Spezia, Mar 14 2024
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: A261016 A328890 A188379 * A248462 A256010 A128543
KEYWORD
nonn,easy,changed
AUTHOR
N. J. A. Sloane, Feb 07 2018
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)