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%I #12 Mar 30 2024 16:17:09
%S 1,8,30,78,162,292,478,731,1061,1478,1992,2614,3354,4222,5228,6383,
%T 7697,9180,10842,12694,14746,17008,19490,22203,25157,28362,31828,
%U 35566,39586,43898,48512,53439,58689,64272,70198,76478,83122,90140,97542,105339,113541
%N Partial sums of A299283.
%H Colin Barker, <a href="/A299284/b299284.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,1,-3,3,-1).
%F From _Colin Barker_, Feb 11 2018: (Start)
%F G.f.: (1 + 5*x + 9*x^2 + 11*x^3 + 9*x^4 + 5*x^5 + x^6) / ((1 - x)^4*(1 + x)*(1 + x^2)).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 3*a(n-5) + 3*a(n-6) - a(n-7) for n>6.
%F (End)
%t LinearRecurrence[{3,-3,1,1,-3,3,-1},{1,8,30,78,162,292,478},50] (* _Harvey P. Dale_, Mar 30 2024 *)
%o (PARI) Vec((1 + 5*x + 9*x^2 + 11*x^3 + 9*x^4 + 5*x^5 + x^6) / ((1 - x)^4*(1 + x)*(1 + x^2)) + O(x^60)) \\ _Colin Barker_, Feb 11 2018
%Y Cf. A299283.
%Y 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.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Feb 10 2018
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