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 A299273 Partial sums of A299272. 51
 1, 7, 25, 62, 125, 224, 366, 555, 804, 1121, 1505, 1973, 2535, 3183, 3939, 4816, 5797, 6910, 8172, 9555, 11094, 12811, 14665, 16699, 18941, 21335, 23933, 26770, 29773, 33004, 36506, 40187, 44120, 48357, 52785, 57489, 62531, 67775, 73319, 79236, 85365, 91818, 98680, 105763, 113194, 121071, 129177 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 Index entries for linear recurrences with constant coefficients, signature (1,0,3,-3,0,-3,3,0,1,-1). FORMULA Conjectures from Colin Barker, Feb 11 2018: (Start) G.f.: (1 + x)^3*(1 + x^2)*(1 + 3*x + 5*x^2 + 3*x^3 + x^4) / ((1 - x)^4*(1 + x + x^2)^3). a(n) = a(n-1) + 3*a(n-3) - 3*a(n-4) - 3*a(n-6) + 3*a(n-7) + a(n-9) - a(n-10) for n>9. (End) These conjectures are correct. - N. J. A. Sloane, Feb 12 2018 MATHEMATICA CoefficientList[Series[(1+x)^3*(1+x^2)*(1+3*x+5*x^2+3*x^3+x^4)/((1-x)^4*(1+x+x^2)^3), {x, 0, 50}], x] (* G. C. Greubel, Feb 20 2018 *) PROG (PARI) x='x+O('x^30); Vec((1+x)^3*(1+x^2)*(1+3*x+5*x^2+3*x^3+x^4)/((1-x)^4*(1+x+x^2)^3)) \\ G. C. Greubel, Feb 20 2018 (MAGMA) Q:=Rationals(); R:=PowerSeriesRing(Q, 40); Coefficients(R!((1+x)^3*(1+x^2)*(1+3*x+5*x^2+3*x^3+x^4)/((1-x)^4*(1+x+x^2)^3))) // G. C. Greubel, Feb 20 2018 CROSSREFS Cf. A299272. 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: A118396 A193375 A185787 * A001845 A127765 A155305 Adjacent sequences:  A299270 A299271 A299272 * A299274 A299275 A299276 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 10 2018 STATUS approved

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Last modified October 14 07:15 EDT 2019. Contains 327995 sequences. (Running on oeis4.)