OFFSET
0,2
COMMENTS
First 20 terms computed byDavide M. Proserpiousing ToposPro.
LINKS
Colin Barker,Table of n, a(n) for n = 0..1000
B. Grünbaum,Uniform tilings of 3-space,Geombinatorics, 4 (1994), 49-56. See tiling #3.
Reticular Chemistry Structure Resource (RCSR),The tcd tiling (or net)
Index entries for linear recurrences with constant coefficients,signature (2,0,-2,1).
FORMULA
G.f.: (x^4 + 8*x^3 + 13*x^2 + 8*x + 1) / ((1 + x)*(1 - x)^3).
FromColin Barker,Feb 11 2018: (Start)
a(n) = (31*n^2 + 8) / 4 for even n>0.
a(n) = (31*n^2 + 9) / 4 for odd n>0.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>4. (End)
E.g.f.: ((8 + 31*x + 31*x^2)*cosh(x) + (9 + 31*x + 31*x^2)*sinh(x) - 4)/4. -Stefano Spezia,Jun 08 2024
MATHEMATICA
LinearRecurrence[{2, 0, -2, 1}, {1, 10, 33, 72, 126}, 50] (*Paolo Xausa,Aug 28 2024 *)
PROG
(PARI) Vec((1 + 8*x + 13*x^2 + 8*x^3 + x^4) / ((1 - x)^3*(1 + x)) + O(x^60)) \\Colin Barker,Feb 11 2018
CROSSREFS
SeeA299288for 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 inA299266for overview.
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane,Feb 10 2018
STATUS
approved