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A299283 Coordination sequence for "svh" 3D uniform tiling. 51
1, 7, 22, 48, 84, 130, 186, 253, 330, 417, 514, 622, 740, 868, 1006, 1155, 1314, 1483, 1662, 1852, 2052, 2262, 2482, 2713, 2954, 3205, 3466, 3738, 4020, 4312, 4614, 4927, 5250, 5583, 5926, 6280, 6644, 7018, 7402, 7797, 8202, 8617, 9042, 9478, 9924, 10380 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

First 20 terms computed by Davide M. Proserpio using ToposPro.

REFERENCES

B. GrĂ¼nbaum, 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

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

See A299284 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.

Sequence in context: A132438 A010001 A197059 * A244243 A223833 A014073

Adjacent sequences:  A299280 A299281 A299282 * A299284 A299285 A299286

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 10 2018

STATUS

approved

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Last modified November 13 11:34 EST 2018. Contains 317133 sequences. (Running on oeis4.)