%I #22 Aug 28 2021 04:48:50
%S 16,35,60,91,128,171,220,275,336,403,476,555,640,731,828,931,1040,
%T 1155,1276,1403,1536,1675,1820,1971,2128,2291,2460,2635,2816,3003,
%U 3196,3395,3600,3811,4028,4251,4480,4715,4956,5203
%N Number of ways to tile a 2n X 2n square with 1 X 1 white and n X n black squares.
%H R. J. Mathar, <a href="http://arxiv.org/abs/1609.03964">Tiling n x m rectangles with 1 x 1 and s x s squares</a>, arXiv:1609.03964 [math.CO], 2016, Section 4.1.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 3*n^2 + 10*n + 3.
%F From _Stefano Spezia_, Aug 18 2020: (Start)
%F O.g.f.: x*(16 - 13*x + 3*x^2)/(1 - x)^3.
%F E.g.f.: exp(x)*(3 + 13*x + 3*x^2) - 3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%e For example, here are two of the 35 ways to tile a 4 X 4 square with 1 X 1 and 2 X 2 squares (where we have dropped the colors):
%e ._______ _______
%e |_|_| | |_|_| |
%e | |___| |_|_|___|
%e |___| | | | |
%e |_|_|___| |_ _|___|
%t Table[3 n^2 + 10 n + 3, {n, 50}] (* _Wesley Ivan Hurt_, Nov 07 2020 *)
%Y Cf. A063443.
%K nonn,easy
%O 1,1
%A _Yutong Li_, Aug 11 2020
%E Edited by _Greg Dresden_, Aug 18 2020