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 A299263 Partial sums of A299257. 51
 1, 6, 18, 40, 76, 132, 214, 325, 469, 652, 878, 1150, 1474, 1856, 2298, 2803, 3379, 4032, 4762, 5572, 6472, 7468, 8558, 9745, 11041, 12452, 13974, 15610, 17374, 19272, 21298, 23455, 25759, 28216, 30818, 33568, 36484, 39572, 42822, 46237, 49837, 53628, 57598 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-8,12,-14,12,-8,4,-1). FORMULA From Colin Barker, Feb 09 2018: (Start) G.f.: (1 + x)*(1 + x + x^2 + 3*x^3 - x^4 + 5*x^5 - 3*x^6 + 4*x^7 - 2*x^8) / ((1 - x)^4*(1 + x^2)^2). a(n) = 4*a(n-1) - 8*a(n-2) + 12*a(n-3) - 14*a(n-4) + 12*a(n-5) - 8*a(n-6) + 4*a(n-7) - a(n-8) for n>8. (End) 5*a(n) = 2*(2*n+1)*(2*n^2+2*n+9)/3 - A138019(n). - R. J. Mathar, Feb 12 2021 PROG (PARI) Vec((1 + x)*(1 + x + x^2 + 3*x^3 - x^4 + 5*x^5 - 3*x^6 + 4*x^7 - 2*x^8) / ((1 - x)^4*(1 + x^2)^2) + O(x^60)) \\ Colin Barker, Feb 09 2018 CROSSREFS Cf. A299257. 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: A002411 A023658 A059834 * A015224 A163983 A191829 Adjacent sequences:  A299260 A299261 A299262 * A299264 A299265 A299266 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 07 2018 STATUS approved

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Last modified January 24 00:05 EST 2022. Contains 350515 sequences. (Running on oeis4.)