OFFSET
0,2
REFERENCES
B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #19.
LINKS
Colin Barker,Table of n, a(n) for n = 0..1000
Reticular Chemistry Structure Resource (RCSR),The ttw tiling (or net)
Index entries for linear recurrences with constant coefficients, signature (3,-5,7,-7,5,-3,1).
FORMULA
G.f.: (2*x^8 - 4*x^7 + 3*x^6 - 5*x^5 + x^4 - 3*x^3 - x^2 - x - 1)*(x + 1) / ((x - 1)^3*(x^2 + 1)^2).
FromColin Barker, Feb 09 2018: (Start)
a(n) = (4 - (2+8*i)*(-i)^n - (2-8*i)*i^n + i*((-i)^n-i^n)*n + 18*n^2) / 8 for n>2, where i=sqrt(-1).
a(n) = 3*a(n-1) - 5*a(n-2) + 7*a(n-3) - 7*a(n-4) + 5*a(n-5) - 3*a(n-6) + a(n-7) for n>9. (End)
MATHEMATICA
LinearRecurrence[{3, -5, 7, -7, 5, -3, 1}, {1, 5, 12, 22, 36, 56, 82, 111, 144, 183}, 60] (*Paolo Xausa, Jun 20 2024 *)
PROG
(PARI) Vec((1 + x)*(1 + x + x^2 + 3*x^3 - x^4 + 5*x^5 - 3*x^6 + 4*x^7 - 2*x^8) / ((1 - x)^3*(1 + x^2)^2) + O(x^60)) \\Colin Barker, Feb 09 2018
CROSSREFS
Cf.A250122.
Partial sums:A299263.
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 inA299266 for overview.
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 07 2018
STATUS
approved