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Partial sums of A299287.
51

%I #9 Feb 12 2018 12:34:55

%S 1,11,44,116,242,438,719,1101,1599,2229,3006,3946,5064,6376,7897,9643,

%T 11629,13871,16384,19184,22286,25706,29459,33561,38027,42873,48114,

%U 53766,59844,66364,73341,80791,88729,97171,106132,115628,125674,136286,147479,159269

%N Partial sums of A299287.

%H Colin Barker, <a href="/A299288/b299288.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 11 2018: (Start)

%F G.f.: (1 + 8*x + 13*x^2 + 8*x^3 + x^4) / ((1 - x)^4*(1 + x)).

%F a(n) = (62*n^3 + 93*n^2 + 82*n + 24) / 24 for n even.

%F a(n) = (62*n^3 + 93*n^2 + 82*n + 27) / 24 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>4.

%F (End)

%o (PARI) Vec((1 + 8*x + 13*x^2 + 8*x^3 + x^4) / ((1 - x)^4*(1 + x)) + O(x^60)) \\ _Colin Barker_, Feb 11 2018

%Y Cf. A299287.

%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