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A299287 Coordination sequence for "tcd" 3D uniform tiling. 51


%S 1,10,33,72,126,196,281,382,498,630,777,940,1118,1312,1521,1746,1986,

%T 2242,2513,2800,3102,3420,3753,4102,4466,4846,5241,5652,6078,6520,

%U 6977,7450,7938,8442,8961,9496,10046,10612,11193,11790,12402,13030,13673,14332

%N Coordination sequence for "tcd" 3D uniform tiling.

%C First 20 terms computed by _Davide M. Proserpio_ using ToposPro.

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

%H Colin Barker, <a href="/A299287/b299287.txt">Table of n, a(n) for n = 0..1000</a>

%H Reticular Chemistry Structure Resource (RCSR), <a href="http://rcsr.net/nets/tcd">The tcd tiling (or net)</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).

%F G.f.: (x^4 + 8*x^3 + 13*x^2 + 8*x + 1) / ((1 + x)*(1 - x)^3).

%F From _Colin Barker_, Feb 11 2018: (Start)

%F a(n) = (31*n^2 + 8) / 4 for n>0.

%F a(n) = (31*n^2 + 9) / 4 for n>0.

%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4.

%F (End)

%o (PARI) Vec((1 + 8*x + 13*x^2 + 8*x^3 + x^4) / ((1 - x)^3*(1 + x)) + O(x^60)) \\ _Colin Barker_, Feb 11 2018

%Y See A299288 for partial sums.

%Y 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.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Feb 10 2018

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Last modified January 21 08:09 EST 2020. Contains 331104 sequences. (Running on oeis4.)