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A299287 Coordination sequence for "tcd" 3D uniform tiling. 51
1, 10, 33, 72, 126, 196, 281, 382, 498, 630, 777, 940, 1118, 1312, 1521, 1746, 1986, 2242, 2513, 2800, 3102, 3420, 3753, 4102, 4466, 4846, 5241, 5652, 6078, 6520, 6977, 7450, 7938, 8442, 8961, 9496, 10046, 10612, 11193, 11790, 12402, 13030, 13673, 14332 (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 #3.

LINKS

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

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

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

G.f.: (x^4 + 8*x^3 + 13*x^2 + 8*x + 1) / ((1 + x)*(1 - x)^3).

From Colin Barker, Feb 11 2018: (Start)

a(n) = (31*n^2 + 8) / 4 for even n>0.

a(n) = (31*n^2 + 9) / 4 for odd n>0.

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.

(End)

PROG

(PARI) Vec((1 + 8*x + 13*x^2 + 8*x^3 + x^4) / ((1 - x)^3*(1 + x)) + O(x^60)) \\ Colin Barker, Feb 11 2018

CROSSREFS

See A299288 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: A348427 A063160 A065149 * A299285 A081437 A085490

Adjacent sequences:  A299284 A299285 A299286 * A299288 A299289 A299290

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 10 2018

STATUS

approved

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)