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A299255 Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3.3.4.3.4 2D tiling (cf. A219529). 51
1, 7, 23, 50, 87, 135, 194, 263, 343, 434, 535, 647, 770, 903, 1047, 1202, 1367, 1543, 1730, 1927, 2135, 2354, 2583, 2823, 3074, 3335, 3607, 3890, 4183, 4487, 4802, 5127, 5463, 5810, 6167, 6535, 6914, 7303, 7703, 8114, 8535, 8967, 9410, 9863, 10327, 10802, 11287, 11783, 12290, 12807, 13335 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

B. Gr├╝nbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #14.

LINKS

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

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

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

FORMULA

G.f.: (x + 1)^5 / ((x^2 + x + 1)*(1 - x)^3).

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n>5. - Colin Barker, Feb 09 2018

MATHEMATICA

LinearRecurrence[{2, -1, 1, -2, 1}, {1, 7, 23, 50, 87, 135}, 60] (* Harvey P. Dale, Apr 01 2018 *)

PROG

(PARI) Vec((1 + x)^5 / ((1 - x)^3*(1 + x + x^2)) + O(x^60)) \\ Colin Barker, Feb 09 2018

CROSSREFS

Cf. A219529.

See A299261 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: A062725 A147121 A098334 * A038796 A332492 A304724

Adjacent sequences:  A299252 A299253 A299254 * A299256 A299257 A299258

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 07 2018

STATUS

approved

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Last modified January 24 19:10 EST 2021. Contains 340411 sequences. (Running on oeis4.)