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%I #12 Oct 03 2018 17:02:23
%S 1,6,19,44,85,147,236,357,514,711,953,1246,1595,2004,2477,3019,3636,
%T 4333,5114,5983,6945,8006,9171,10444,11829,13331,14956,16709,18594,
%U 20615,22777,25086,27547,30164,32941,35883,38996,42285,45754,49407,53249,57286,61523
%N Partial sums of A299258.
%C Euler transform of length 6 sequence [6, -2, 0, 0, 1, -1]. - _Michael Somos_, Oct 03 2018
%H Colin Barker, <a href="/A299264/b299264.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,1,-3,3,-1).
%F From _Colin Barker_, Feb 09 2018: (Start)
%F G.f.: (1 + x)^3*(1 - x + x^2)*(1 + x + x^2) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8) for n>7.
%F (End)
%F a(n) = -a(-1-n) for all n in Z. - _Michael Somos_, Oct 03 2018
%e G.f. = 1 + 6*x + 19*x^2 + 44*x^3 + 85*x^4 + 147*x^5 + 236*x^6 + ... - _Michael Somos_, Oct 03 2018
%t a[ n_] := (4 n^3 + 6 n^2 + 16 n + {5, 4, 7, 10, 9}[[Mod[n, 5] + 1]]) / 5; (* _Michael Somos_, Oct 03 2018 *)
%o (PARI) Vec((1 + x)^3*(1 - x + x^2)*(1 + x + x^2) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ _Colin Barker_, Feb 09 2018
%o (PARI) {a(n) = (4*n^3 + 6*n^2 + 16*n + [5, 4, 7, 10, 9][n%5+1]) / 5}; /* _Michael Somos_, Oct 03 2018 */
%Y Cf. A299258.
%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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