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A299254
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Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3^4.6 2D tiling (cf. A250120).
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51
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1, 7, 21, 45, 79, 122, 175, 237, 309, 391, 482, 583, 693, 813, 943, 1082, 1231, 1389, 1557, 1735, 1922, 2119, 2325, 2541, 2767, 3002, 3247, 3501, 3765, 4039, 4322, 4615, 4917, 5229, 5551, 5882, 6223, 6573, 6933, 7303, 7682, 8071, 8469, 8877, 9295, 9722, 10159, 10605, 11061, 11527, 12002
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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 #17.
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
Reticular Chemistry Structure Resource (RCSR), The svj tiling (or net)
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1).
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FORMULA
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G.f.: (x^2+x+1)*(x^4+3*x^3+3*x+1)*(x+1) / ((x^4+x^3+x^2+x+1)*(1-x)^3). (This is the product of the g.f.'s for A250120 and A040000. - N. J. A. Sloane, Nov 10 2018)
a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7) for n>7. - Colin Barker, Feb 07 2018
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PROG
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(PARI) Vec((1 + x)*(1 + x + x^2)*(1 + 3*x + 3*x^3 + x^4) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ Colin Barker, Feb 07 2018
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CROSSREFS
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Cf. A040000, A250120.
Partial sums: A299260.
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: A077354 A246430 A256051 * A146411 A287431 A127736
Adjacent sequences: A299251 A299252 A299253 * A299255 A299256 A299257
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Feb 06 2018
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STATUS
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approved
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