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 #8.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
V. A. Blatov, A. P. Shevchenko, D. M. Proserpio, Applied Topological Analysis of Crystal Structures with the Program Package ToposPro, Cryst. Growth Des. 2014, 14, 3576-3586.
Reticular Chemistry Structure Resource (RCSR), The cab tiling (or net)
Davide M. Proserpio, Summary of the 28 uniform 3D tilings and their coordination sequences (produced by ToposPro)
Index entries for linear recurrences with constant coefficients, signature (1,-1,2,0,0,0,-2,1,-1,1).
FORMULA
G.f.: (4*x^12 -4*x^11 +x^10 +5*x^8 +20*x^7 +18*x^6 +24*x^5 +14*x^4 +16*x^3 +5*x^2 +4*x +1)/((1-x)*(1-x^2)*(1-x^3)*(1+x^2)^2). - N. J. A. Sloane, Feb 12 2018
a(n) = a(n-1) - a(n-2) + 2*a(n-3) - 2*a(n-7) + a(n-8) - a(n-9) + a(n-10) for n>12. - Colin Barker, Feb 15 2018
MATHEMATICA
CoefficientList[Series[(4*x^12-4*x^11+x^10+5*x^8+20*x^7+18*x^6+24*x^5 +14*x^4+16*x^3+5*x^2+4*x+1)/((1-x)*(1-x^2)*(1-x^3)*(1+x^2)^2), {x, 0, 50}], x] (* G. C. Greubel, Feb 20 2018 *)
PROG
(PARI) Vec((1 + 4*x + 5*x^2 + 16*x^3 + 14*x^4 + 24*x^5 + 18*x^6 + 20*x^7 + 5*x^8 + x^10 - 4*x^11 + 4*x^12) / ((1 - x)^3*(1 + x)*(1 + x^2)^2*(1 + x + x^2)) + O(x^60)) \\ Colin Barker, Feb 15 2018
(Magma) I:=[22, 37, 57, 82, 117, 145, 178, 229, 281, 322]; [1, 5, 9] cat [n le 10 select I[n] else Self(n-1) -Self(n-2) +2*Self(n-3)-2*Self(n-7)+Self(n-8)-Self(n-9) + Self(n-10): n in [1..30]]; // G. C. Greubel, Feb 20 2018
CROSSREFS
See A299267 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
AUTHOR
N. J. A. Sloane, Feb 07 2018
EXTENSIONS
a(21)-a(40) from Davide M. Proserpio, Feb 12 2018
STATUS
approved