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A299279 Coordination sequence for "reo" 3D uniform tiling. 51
1, 8, 30, 68, 126, 180, 286, 348, 510, 572, 798, 852, 1150, 1188, 1566, 1580, 2046, 2028, 2590, 2532, 3198, 3092, 3870, 3708, 4606, 4380, 5406, 5108, 6270, 5892, 7198, 6732, 8190, 7628, 9246, 8580, 10366, 9588, 11550, 10652, 12798, 11772, 14110, 12948, 15486, 14180 (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 #7.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Reticular Chemistry Structure Resource (RCSR), The reo tiling (or net)

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

FORMULA

G.f.: (4*x^7 - 3*x^6 + 39*x^4 + 44*x^3 + 27*x^2 + 8*x + 1) / (1 - x^2)^3.

From Colin Barker, Feb 11 2018: (Start)

a(n) = 8*n^2 - 2 for n>1.

a(n) = 7*n^2 + 5 for n>1.

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>7.

(End)

PROG

(PARI) Vec((1 + 8*x + 27*x^2 + 44*x^3 + 39*x^4 - 3*x^6 + 4*x^7) / ((1 - x)^3*(1 + x)^3) + O(x^60)) \\ Colin Barker, Feb 11 2018

CROSSREFS

See A299280 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: A074670 A092277 A008469 * A184323 A004639 A317637

Adjacent sequences:  A299276 A299277 A299278 * A299280 A299281 A299282

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 10 2018

STATUS

approved

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Last modified November 15 11:35 EST 2018. Contains 317238 sequences. (Running on oeis4.)