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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. Gr├╝nbaum, 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 October 15 08:45 EDT 2018. Contains 316210 sequences. (Running on oeis4.)