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A299260 Partial sums of A299254. 51

%I

%S 1,8,29,74,153,275,450,687,996,1387,1869,2452,3145,3958,4901,5983,

%T 7214,8603,10160,11895,13817,15936,18261,20802,23569,26571,29818,

%U 33319,37084,41123,45445,50060,54977,60206,65757,71639,77862,84435,91368,98671,106353

%N Partial sums of A299254.

%H Colin Barker, <a href="/A299260/b299260.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)*(1 + x + x^2)*(1 + 3*x + 3*x^3 + x^4) / ((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)

%o (PARI) Vec((1 + x)*(1 + x + x^2)*(1 + 3*x + 3*x^3 + x^4) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ _Colin Barker_, Feb 09 2018

%Y Cf. A299254.

%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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Last modified December 9 03:27 EST 2019. Contains 329872 sequences. (Running on oeis4.)