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%I #13 Mar 14 2024 16:31:09
%S 1,7,25,65,137,249,411,631,919,1283,1733,2277,2925,3685,4567,5579,
%T 6731,8031,9489,11113,12913,14897,17075,19455,22047,24859,27901,31181,
%U 34709,38493,42543,46867,51475,56375,61577,67089,72921,79081,85579,92423,99623,107187,115125,123445,132157,141269,150791,160731,171099
%N Partial sums of A299256.
%H Colin Barker, <a href="/A299262/b299262.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F From _Colin Barker_, Feb 09 2018: (Start)
%F G.f.: (1 + 2*x)*(1 + 2*x + 2*x^2 + 2*x^3 - x^4) / ((1 - x)^4*(1 + x)).
%F a(n) = (6*n^3 + 9*n^2 + 2*n + 12) / 4 for n>0 and even.
%F a(n) = (6*n^3 + 9*n^2 + 2*n + 11) / 4 for n odd.
%F a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) for n>5. (End)
%F E.g.f.: ((12 + 17*x + 27*x^2 + 6*x^3)*cosh(x) + (11 + 17*x + 27*x^2 + 6*x^3)*sinh(x) - 8)/4. - _Stefano Spezia_, Mar 14 2024
%o (PARI) Vec((1 + 2*x)*(1 + 2*x + 2*x^2 + 2*x^3 - x^4) / ((1 - x)^4*(1 + x)) + O(x^60)) \\ _Colin Barker_, Feb 09 2018
%Y Cf. A299256.
%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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