A299283 Coordination sequence for "svh" 3D uniform tiling.
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
Offset: 0
References
- B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #15.
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Reticular Chemistry Structure Resource (RCSR), The svh tiling (or net)
- Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).
Crossrefs
See A299284 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.
Programs
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Mathematica
LinearRecurrence[{2,-1,0,1,-2,1},{1,7,22,48,84,130,186},50] (* Harvey P. Dale, May 19 2019 *) -
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
Formula
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
a(n) = (29 - (-1)^n + 82*n^2 + 4*A056594(n))/16 for n > 0. - Stefano Spezia, Jun 06 2024
Comments