A299278 Partial sums of A299277.

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

Colin Barker, Table of n, a(n) for n = 0..1000

V. A. Blatov, A. P. Shevchenko, and 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 (3,-6,11,-17,24,-30,34,-36,34,-30,24,-17,11,-6,3,-1).

Formula

G.f.: (1 + 3*x + 7*x^2 + 13*x^3 + 21*x^4 + 30*x^5 + 36*x^6 + 42*x^7 + 44*x^8 + 40*x^9 + 34*x^10 + 23*x^11 + 12*x^12 + 5*x^13 - 2*x^15 - x^16 + x^17 + 2*x^18 + x^19)/((1 - x)^4*(1 + x^2)*(1 - x + x^2)^2*(1 + x + x^2)^3). - N. J. A. Sloane, Feb 13 2018 [simplified by Stefano Spezia, Feb 27 2026]

a(n) = 3*a(n-1) - 6*a(n-2) + 11*a(n-3) - 17*a(n-4) + 24*a(n-5) - 30*a(n-6) + 34*a(n-7) - 36*a(n-8) + 34*a(n-9) - 30*a(n-10) + 24*a(n-11) - 17*a(n-12) + 11*a(n-13) - 6*a(n-14) + 3*a(n-15) - a(n-16) for n >= 20. - Colin Barker, Feb 14 2018 [simplified by Paolo Xausa, Feb 27 2026]

Mathematica

LinearRecurrence[{3, -6, 11, -17, 24, -30, 34, -36, 34, -30, 24, -17, 11, -6, 3, -1}, {1, 6, 19, 45, 91, 164, 268, 408, 595, 835, 1127, 1479, 1896, 2378, 2945, 3605, 4345, 5183, 6127, 7158}, 50] (* Paolo Xausa, Feb 26 2026 *)

Prog

(PARI) Vec((1 + 3*x + 7*x^2 + 13*x^3 + 21*x^4 + 30*x^5 + 36*x^6 + 42*x^7 + 44*x^8 + 40*x^9 + 34*x^10 + 23*x^11 + 12*x^12 + 5*x^13 - 2*x^15 - x^16 + x^17 + 2*x^18 + x^19)/((1 - x)^4*(1 + x^2)*(1 - x + x^2)^2*(1 + x + x^2)^3) + O(x^60)) \\ Colin Barker, Feb 14 2018 [simplified by Stefano Spezia, Feb 27 2026]

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

Adjacent sequences: A299275 A299276 A299277 * A299279 A299280 A299281

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 10 2018

Status

approved