OFFSET
0,2
COMMENTS
First 20 terms computed by Davide M. Proserpio using ToposPro.
REFERENCES
B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #7.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Reticular Chemistry Structure Resource (RCSR), The reo tiling (or net)
Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
FORMULA
G.f.: (4*x^7 - 3*x^6 + 39*x^4 + 44*x^3 + 27*x^2 + 8*x + 1) / (1 - x^2)^3.
From Colin Barker, Feb 11 2018: (Start)
a(n) = 8*n^2 - 2 for even n > 1.
a(n) = 7*n^2 + 5 for odd n > 1.
a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>7. (End)
E.g.f.: 3 - 4*x + (8*x^2 + 7*x - 2)*cosh(x) + (7*x^2 + 8*x + 5)*sinh(x). - Stefano Spezia, Jun 06 2024
MATHEMATICA
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {1, 8, 30, 68, 126, 180, 286, 348}, 50] (* Paolo Xausa, Jan 16 2025 *)
PROG
(PARI) Vec((1 + 8*x + 27*x^2 + 44*x^3 + 39*x^4 - 3*x^6 + 4*x^7) / ((1 - x)^3*(1 + x)^3) + O(x^60)) \\ Colin Barker, Feb 11 2018
CROSSREFS
See A299280 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.
KEYWORD
nonn,easy,changed
AUTHOR
N. J. A. Sloane, Feb 10 2018
STATUS
approved