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A299278
Partial sums of A299277.
51
1, 6, 19, 45, 91, 164, 268, 408, 595, 835, 1127, 1479, 1896, 2378, 2945, 3605, 4345, 5183, 6127, 7158, 8308, 9598, 10997, 12528, 14205, 15992, 17936, 20066, 22327, 24758, 27382, 30132, 33073, 36253, 39587, 43125, 46902, 50822, 54971, 59411, 64021, 68873, 74017, 79314, 84874
OFFSET
0,2
COMMENTS
First 80 terms computed by Davide M. Proserpio using ToposPro.
LINKS
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 pcu-i tiling (or net)
Index entries for linear recurrences with constant coefficients, signature (1,-1,2,-1,1,1,-2,2,-4,2,-2,1,1,-1,2,-1,1,-1).
FORMULA
G.f.: (x^16 - x^15 + x^14 - 2*x^13 + 2*x^12 - x^11 + 4*x^10 + x^9 + 9*x^8 + 12*x^6 - x^5 + 9*x^4 + 4*x^2 + 1) * (x + 1)^5 / ((1 - x)*(1 + x^2)*(1 - x^3)*(1 - x^6)^2). - N. J. A. Sloane, Feb 13 2018
a(n) = a(n-1) - a(n-2) + 2*a(n-3) - a(n-4) + a(n-5) + a(n-6) - 2*a(n-7) + 2*a(n-8) - 4*a(n-9) + 2*a(n-10) - 2*a(n-11) + a(n-12) + a(n-13) - a(n-14) + 2*a(n-15) - a(n-16) + a(n-17) - a(n-18) for n>21. - Colin Barker, Feb 14 2018
PROG
(PARI) Vec((x^16 - x^15 + x^14 - 2*x^13 + 2*x^12 - x^11 + 4*x^10 + x^9 + 9*x^8 + 12*x^6 - x^5 + 9*x^4 + 4*x^2 + 1) * (x + 1)^5 / ((1 - x)*(1 + x^2)*(1 - x^3)*(1 - x^6)^2) + O(x^60)) \\ Colin Barker, Feb 14 2018
CROSSREFS
Cf. A299277.
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: A362602 A299265 A005712 * A298741 A070893 A272047
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 10 2018
STATUS
approved