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A299255
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Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3.3.4.3.4 2D tiling (cf. A219529).
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51
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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
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OFFSET
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0,2
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REFERENCES
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B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #14.
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LINKS
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FORMULA
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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
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MATHEMATICA
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LinearRecurrence[{2, -1, 1, -2, 1}, {1, 7, 23, 50, 87, 135}, 60] (* Harvey P. Dale, Apr 01 2018 *)
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PROG
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(PARI) Vec((1 + x)^5 / ((1 - x)^3*(1 + x + x^2)) + O(x^60)) \\ Colin Barker, Feb 09 2018
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CROSSREFS
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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.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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