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A299282 Partial sums of A299281. 51

%I #19 Apr 23 2023 13:06:41

%S 1,7,26,67,139,253,419,643,931,1295,1749,2299,2947,3705,4591,5611,

%T 6763,8059,9521,11155,12955,14933,17115,19507,22099,24903,27949,31243,

%U 34771,38545,42599,46939,51547,56435,61641,67171,73003,79149,85651,92515,99715,107263,115205

%N Partial sums of A299281.

%H Colin Barker, <a href="/A299282/b299282.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 (4,-8,12,-14,12,-8,4,-1).

%F From _Colin Barker_, Feb 14 2018: (Start)

%F G.f.: (1 + x)*(1 + x^2 + x^3)*(1 + 2*x + 3*x^2 + x^4 - 2*x^5 + x^6) / ((1 - x)^4*(1 + x^2)^2).

%F a(n) = 4*a(n-1) - 8*a(n-2) + 12*a(n-3) - 14*a(n-4) + 12*a(n-5) - 8*a(n-6) + 4*a(n-7) - a(n-8) for n>8. (End)

%F a(n) = (n*(6*n^2 + 9*n + 11) - 12 + (n - 8)*A056594(n) - (n + 1)*A056594(n+1))/4 for n > 2. - _Stefano Spezia_, Apr 23 2023

%o (PARI) Vec((1 + x)*(1 + x^2 + x^3)*(1 + 2*x + 3*x^2 + x^4 - 2*x^5 + x^6) / ((1 - x)^4*(1 + x^2)^2) + O(x^70)) \\ _Colin Barker_, Feb 14 2018

%Y Cf. A056594, A299281.

%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

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)