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A299283
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Coordination sequence for "svh" 3D uniform tiling.
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51
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1, 7, 22, 48, 84, 130, 186, 253, 330, 417, 514, 622, 740, 868, 1006, 1155, 1314, 1483, 1662, 1852, 2052, 2262, 2482, 2713, 2954, 3205, 3466, 3738, 4020, 4312, 4614, 4927, 5250, 5583, 5926, 6280, 6644, 7018, 7402, 7797, 8202, 8617, 9042, 9478, 9924, 10380
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OFFSET
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0,2
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COMMENTS
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REFERENCES
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B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #15.
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LINKS
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FORMULA
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G.f.: (x^6+5*x^5+9*x^4+11*x^3+9*x^2+5*x+1)/((x+1)*(x^2+1)*(1-x)^3).
a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) for n>6. - Colin Barker, Feb 11 2018
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MATHEMATICA
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LinearRecurrence[{2, -1, 0, 1, -2, 1}, {1, 7, 22, 48, 84, 130, 186}, 50] (* Harvey P. Dale, May 19 2019 *)
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PROG
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(PARI) Vec((1 + 5*x + 9*x^2 + 11*x^3 + 9*x^4 + 5*x^5 + x^6) / ((1 - x)^3*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Feb 11 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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