This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A338996 #26 Dec 23 2020 07:39:33
%S A338996 0,5,27,85,205,420,770,1302,2070,3135,4565,6435,8827,11830,15540,
%T A338996 20060,25500,31977,39615,48545,58905,70840,84502,100050,117650,137475,
%U A338996 159705,184527,212135,242730,276520
%N A338996 Numbers of squares and rectangles of all sizes in 3*n*(n+1)/2-ominoes in form of three-quarters of Aztec diamonds.
%H A338996 Luce ETIENNE, <a href="/A338996/a338996.pdf">Illustration of a(1), a(2), a(3) and a(4)</a>
%H A338996 Wikipedia, <a href="https://en.wikipedia.org/wiki/Aztec_diamond">Aztec diamond</a>.
%H A338996 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A338996 G.f.: x*(2*x + 5)/(1 - x)^5.
%F A338996 E.g.f.: exp(x)*x*(120 + 204*x + 76*x^2 + 7*x^3)/24. - _Stefano Spezia_, Nov 18 2020
%F A338996 a(n) = 5*(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F A338996 a(n) = n*(n + 1)*(n + 2)*(7*n + 13)/24.
%F A338996 a(n) = 2*A004320(n) - A000332(n+3).
%F A338996 a(n) = 2*A000332(n+2) + 5*A000332(n+3).
%e A338996 a(1) = 2*3-1 = 5, a(2) = 2*16-5 = 27, a(3) = 2*50-15 = 85, a(4) = 2*120-35 = 205, a(5) = 2*245-70 = 420, a(6) = 2*448-126 = 770.
%t A338996 CoefficientList[Series[x (2 x + 5)/(1 - x)^5, {x, 0, 30}], x] (* _Michael De Vlieger_, Dec 12 2020 *)
%Y A338996 Cf. A000217, A000332, A002417, A004320, A045943, A258440, A330805.
%K A338996 nonn,easy
%O A338996 0,2
%A A338996 _Luce ETIENNE_, Nov 18 2020