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A299291 Coordination sequence for "ubt" 3D uniform tiling. 51
1, 5, 14, 29, 56, 85, 130, 181, 226, 299, 382, 445, 538, 635, 708, 845, 962, 1079, 1218, 1363, 1456, 1671, 1808, 1987, 2170, 2365, 2470, 2777, 2920, 3169, 3394, 3641, 3750, 4163, 4298, 4625, 4890, 5191, 5296, 5829, 5942, 6355, 6658, 7015, 7108, 7775, 7852, 8359, 8698, 9113, 9186 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

First 80 terms computed by Davide M. Proserpio using ToposPro.

REFERENCES

B. Gr├╝nbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #10.

LINKS

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

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

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

FORMULA

G.f.: (12*x^20 + 16*x^19 - 20*x^17 - 27*x^16 - 8*x^15 + 3*x^14 + 46*x^13 + 115*x^12 + 176*x^11 + 212*x^10 + 226*x^9 + 228*x^8 + 214*x^7 + 170*x^6 + 122*x^5 + 79*x^4 + 42*x^3 + 19*x^2 + 6*x + 1) / ((1 + x)*(1 - x^3)*(1 - x^6)^2). - N. J. A. Sloane, Feb 13 2018

a(n) = -a(n-1) + a(n-3) + a(n-4) + 2*a(n-6) + 2*a(n-7) - 2*a(n-9) - 2*a(n-10) - a(n-12) - a(n-13) + a(n-15) + a(n-16) for n>17. - Colin Barker, Feb 14 2018

PROG

(PARI) Vec((12*x^20 + 16*x^19 - 20*x^17 - 27*x^16 - 8*x^15 + 3*x^14 + 46*x^13 + 115*x^12 + 176*x^11 + 212*x^10 + 226*x^9 + 228*x^8 + 214*x^7 + 170*x^6 + 122*x^5 + 79*x^4 + 42*x^3 + 19*x^2 + 6*x + 1) / ((1 + x)*(1 - x^3)*(1 - x^6)^2) + O(x^50)) \\ Colin Barker, Feb 14 2018

CROSSREFS

See A299292 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: A256666 A319007 A211651 * A019262 A212919 A280230

Adjacent sequences:  A299288 A299289 A299290 * A299292 A299293 A299294

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 10 2018

STATUS

approved

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Last modified November 12 19:19 EST 2018. Contains 317116 sequences. (Running on oeis4.)