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%I #12 Oct 03 2018 16:47:27
%S 1,8,31,81,168,303,497,760,1103,1537,2072,2719,3489,4392,5439,6641,
%T 8008,9551,11281,13208,15343,17697,20280,23103,26177,29512,33119,
%U 37009,41192,45679,50481,55608,61071,66881,73048,79583,86497,93800,101503,109617
%N Partial sums of A299255.
%C Euler transform of length 3 sequence [8, -5, 1]. - _Michael Somos_, Oct 03 2018
%H Colin Barker, <a href="/A299261/b299261.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,2,-3,3,-1).
%F From _Colin Barker_, Feb 09 2018: (Start)
%F G.f.: (1 + x)^5 / ((1 - x)^4*(1 + x + x^2)).
%F a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 3*a(n-4) + 3*a(n-5) - a(n-6) for n>5.
%F (End)
%F a(n) = -a(-1-n) for all n in Z. - _Michael Somos_, Oct 03 2018
%t a[ n_] := (8 (2 n + 1) (n^2 + n + 1) - Mod[n - 1, 3, -1]) / 9; (* _Michael Somos_, Oct 03 2018 *)
%o (PARI) Vec((1 + x)^5 / ((1 - x)^4*(1 + x + x^2)) + O(x^60)) \\ _Colin Barker_, Feb 09 2018
%o (PARI) {a(n) = (8 * (2*n + 1) * (n^2 + n + 1) + (n%3==0) - (n%3==2)) / 9}; /* _Michael Somos_, Oct 03 2018 */
%Y Cf. A299255.
%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 07 2018
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