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 A299256 Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3.6.3.6 2D tiling (cf. A008579). 51
 1, 6, 18, 40, 72, 112, 162, 220, 288, 364, 450, 544, 648, 760, 882, 1012, 1152, 1300, 1458, 1624, 1800, 1984, 2178, 2380, 2592, 2812, 3042, 3280, 3528, 3784, 4050, 4324, 4608, 4900, 5202, 5512, 5832, 6160, 6498, 6844, 7200, 7564, 7938, 8320, 8712, 9112, 9522, 9940, 10368, 10804, 11250, 11704 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #18. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Reticular Chemistry Structure Resource (RCSR), The kag tiling (or net) Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA G.f.: (1 + 2*x)*(x^4 - 2*x^3 - 2*x^2 - 2*x - 1) / ((x - 1)^3*(x + 1)). From Colin Barker, Feb 09 2018: (Start) a(n) = 9*n^2 / 2 for n>1. a(n) = (9*n^2 - 1) / 2 for n>1. a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>5. (End) MAPLE seq(coeff(series((1+2*x)*(x^4-2*x^3-2*x^2-2*x-1)/((x-1)^3*(1+x)), x, n+1), x, n), n = 0 .. 35); # Muniru A Asiru, Oct 26 2018 MATHEMATICA Join[{1, 6}, LinearRecurrence[{2, 0, -2, 1}, {18, 40, 72, 112}, 50]] (* Vincenzo Librandi, Oct 26 2018 *) PROG (PARI) Vec((1 + 2*x)*(1 + 2*x + 2*x^2 + 2*x^3 - x^4) / ((1 - x)^3*(1 + x)) + O(x^60)) \\ Colin Barker, Feb 09 2018 (MAGMA) [1, 6] cat [9*n^2 div 2: n in [2..50]]; // Vincenzo Librandi, Oct 26 2018 (GAP) a:=[18, 40, 72, 112];; for n in [5..50] do a[n]:=2*a[n-1]-2*a[n-3]+a[n-4]; od; Concatenation([1, 6], a); # Muniru A Asiru, Oct 26 2018 CROSSREFS Cf. A008579. For partial sums see A299262. 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: A219143 A122061 A333713 * A002411 A023658 A059834 Adjacent sequences:  A299253 A299254 A299255 * A299257 A299258 A299259 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 07 2018 STATUS approved

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Last modified January 24 18:36 EST 2021. Contains 340411 sequences. (Running on oeis4.)