%I #19 Sep 08 2022 08:46:20

%S 1,6,15,37,74,131,213,330,475,653,882,1163,1485,1862,2307,2821,3398,

%T 4043,4773,5598,6499,7481,8574,9779,11073,12470,13995,15649,17414,

%U 19295,21321,23502,25807,28241,30846,33623,36537,39602,42855,46297,49898,53663,57633,61818,66175,70709,75474,80471,85653,91034,96663

%N Partial sums of A299266.

%H Colin Barker, <a href="/A299267/b299267.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,3,-2,0,0,-2,3,-2,2,-1).

%F From _Colin Barker_, Feb 15 2018: (Start)

%F G.f.: (1 +4*x +5*x^2 +16*x^3 +14*x^4 +24*x^5 +18*x^6 +20*x^7 +5*x^8 + x^10 -4*x^11 +4*x^12)/((1 -x)^4*(1 +x)*(1 +x^2)^2*(1 +x +x^2)).

%F a(n) = 2*a(n-1) - 2*a(n-2) + 3*a(n-3) - 2*a(n-4) - 2*a(n-7) + 3*a(n-8) - 2*a(n-9) + 2*a(n-10) - a(n-11) for n>12.

%F (End)

%t CoefficientList[Series[(1 +4*x +5*x^2 +16*x^3 +14*x^4 +24*x^5 +18*x^6 +20*x^7 +5*x^8 + x^10 -4*x^11 +4*x^12)/((1 -x)^4*(1 +x)*(1 +x^2)^2*(1 +x +x^2)), {x, 0, 50}], x] (* _G. C. Greubel_, Feb 20 2018 *)

%t LinearRecurrence[{2,-2,3,-2,0,0,-2,3,-2,2,-1},{1,6,15,37,74,131,213,330,475,653,882,1163,1485},60] (* _Harvey P. Dale_, Sep 03 2018 *)

%o (PARI) Vec((1 + 4*x + 5*x^2 + 16*x^3 + 14*x^4 + 24*x^5 + 18*x^6 + 20*x^7 + 5*x^8 + x^10 - 4*x^11 + 4*x^12) / ((1 - x)^4*(1 + x)*(1 + x^2)^2*(1 + x + x^2)) + O(x^60)) \\ _Colin Barker_, Feb 15 2018

%o (Magma) I:=[15,37,74,131,213,330,475,653,882,1163,1485]; [1,6] cat [n le 11 select I[n] else 2*Self(n-1) -2*Self(n-2) +3*Self(n-3)-2*Self(n-4)-2*Self(n-7) +3*Self(n-8) -2*Self(n-9)+2*Self(n-10)-Self(n-11): n in [1..30]]; // _G. C. Greubel_, Feb 20 2018

%Y Cf. A299266.

%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