OFFSET
0,2
COMMENTS
First 20 terms computed byDavide M. Proserpio using ToposPro.
REFERENCES
B. Grünbaum, Uniform tilings of 3-space, Geombinatorics, 4 (1994), 49-56. See tiling #15.
LINKS
Colin Barker,Table of n, a(n) for n = 0..1000
Reticular Chemistry Structure Resource (RCSR),The svh tiling (or net)
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).
FORMULA
G.f.: (x^6+5*x^5+9*x^4+11*x^3+9*x^2+5*x+1)/((x+1)*(x^2+1)*(1-x)^3).
a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*a(n-5) + a(n-6) for n>6. -Colin Barker, Feb 11 2018
a(n) = (29 - (-1)^n + 82*n^2 + 4*A056594(n))/16 for n > 0. -Stefano Spezia, Jun 06 2024
MATHEMATICA
LinearRecurrence[{2, -1, 0, 1, -2, 1}, {1, 7, 22, 48, 84, 130, 186}, 50] (*Harvey P. Dale, May 19 2019 *)
PROG
(PARI) Vec((1 + 5*x + 9*x^2 + 11*x^3 + 9*x^4 + 5*x^5 + x^6) / ((1 - x)^3*(1 + x)*(1 + x^2)) + O(x^60)) \\Colin Barker, Feb 11 2018
CROSSREFS
SeeA299284 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 inA299266 for overview.
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 10 2018
STATUS
approved