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A299277 Coordination sequence for "pcu-i" 3D uniform tiling. 51

%I

%S 1,5,13,26,46,73,104,140,187,240,292,352,417,482,567,660,740,838,944,

%T 1031,1150,1290,1399,1531,1677,1787,1944,2130,2261,2431,2624,2750,

%U 2941,3180,3334,3538,3777,3920,4149,4440,4610,4852,5144,5297,5560,5910,6097,6373,6717,6881,7182,7590,7787,8101,8504,8672

%N Coordination sequence for "pcu-i" 3D uniform tiling.

%C First 80 terms computed by _Davide M. Proserpio_ using ToposPro.

%D B. Gr├╝nbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #20.

%H Colin Barker, <a href="/A299277/b299277.txt">Table of n, a(n) for n = 0..1000</a>

%H V. A. Blatov, A. P. Shevchenko, D. M. Proserpio, <a href="http://pubs.acs.org/doi/pdf/10.1021/cg500498k">Applied Topological Analysis of Crystal Structures with the Program Package ToposPro</a>, Cryst. Growth Des. 2014, 14, 3576-3586.

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

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (0,-1,1,0,1,2,0,2,-2,0,-2,-1,0,-1,1,0,1).

%F G.f.: (x^16 - x^15 + x^14 - 2*x^13 + 2*x^12 - x^11 + 4*x^10 + x^9 + 9*x^8 + 12*x^6 - x^5 + 9*x^4 + 4*x^2 + 1) * (x + 1)^5 / ((1 + x^2)*(1 - x^3)*(1 - x^6)^2). - _N. J. A. Sloane_, Feb 13 2018

%F a(n) = -a(n-2) + a(n-3) + a(n-5) + 2*a(n-6) + 2*a(n-8) - 2*a(n-9) - 2*a(n-11) - a(n-12) - a(n-14) + a(n-15) + a(n-17) for n>21. - _Colin Barker_, Feb 14 2018

%o (PARI) Vec((x^16 - x^15 + x^14 - 2*x^13 + 2*x^12 - x^11 + 4*x^10 + x^9 + 9*x^8 + 12*x^6 - x^5 + 9*x^4 + 4*x^2 + 1) * (x + 1)^5 / ((1 + x^2)*(1 - x^3)*(1 - x^6)^2) + O(x^60)) \\ _Colin Barker_, Feb 14 2018

%Y See A299278 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 February 24 18:41 EST 2021. Contains 341577 sequences. (Running on oeis4.)