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%I #12 Jul 22 2021 19:14:35
%S 1,9,39,107,233,413,699,1047,1557,2129,2927,3779,4929,6117,7683,9263,
%T 11309,13337,15927,18459,21657,24749,28619,32327,36933,41313,46719,
%U 51827,58097,63989,71187,77919,86109,93737,102983,111563,121929,131517,143067,153719,166517
%N Partial sums of A299279.
%H Colin Barker, <a href="/A299280/b299280.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 (1,3,-3,-3,3,1,-1).
%F From _Colin Barker_, Feb 11 2018: (Start)
%F G.f.: (1 + 8*x + 27*x^2 + 44*x^3 + 39*x^4 - 3*x^6 + 4*x^7) / ((1 - x)^4*(1 + x)^3).
%F a(n) = (5*n^3 + 8*n^2 + 6*n - 6) / 2 for n>0 and even.
%F a(n) = (5*n^3 + 7*n^2 + 5*n + 1) / 2 for n odd.
%F a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n>7.
%F (End)
%t LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,9,39,107,233,413,699,1047},50] (* _Harvey P. Dale_, Jul 22 2021 *)
%o (PARI) Vec((1 + 8*x + 27*x^2 + 44*x^3 + 39*x^4 - 3*x^6 + 4*x^7) / ((1 - x)^4*(1 + x)^3) + O(x^60)) \\ _Colin Barker_, Feb 11 2018
%Y Cf. A299279.
%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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