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 A105745 #21 May 01 2025 13:13:00
%S A105745 1,12,13,4,9,9,4,5,6,8,8,6,2,4,6,4,2,2,4,6,4,2,2,4,6,4,2,2,4,6,4,2,2,
%T A105745 4,6,4,2,2,4,6,4,2,2,4,6,4,2,2,4,6,4,2,2,4,6,4,2,2,4,6,4,2,2,4,6,4,2,
%U A105745 2,4,6,4,2,2,4,6,4,2,2,4,6,4,2,2,4,6,4,2,2,4,6,4,2,2,4,6,4,2,2,4
%N A105745 For n>2, a(n) > 0 is such that a(n-1)^2+4*a(n-2)*a(n) is a minimal square, a(1)=1, a(2)=12.
%H A105745 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).
%F A105745 a(n)=a(n-5) for n >= 18. - _Robert Israel_, Oct 02 2020
%F A105745 G.f.: x*(4*x^16 + 4*x^15 + 2*x^14 + 2*x^13 + 3*x^12 - 2*x^11 + x^10 + x^9 - 2*x^8 + 8*x^7 + 8*x^6 - 8*x^5 - 9*x^4 - 4*x^3 - 13*x^2 - 12*x - 1)/(x^5 - 1). - _Chai Wah Wu_, May 07 2024
%p A105745 A[1]:= 1: A[2]:= 12:
%p A105745 for n from 3 to 100 do
%p A105745 R:= map(rhs@op, [msolve(y^2=A[n-1]^2, 4*A[n-2])]);
%p A105745 ys:= map(t -> (floor((A[n-1]-t)/(4*A[n-2]))+1)*4*A[n-2]+t, R);
%p A105745 A[n]:= (min(ys)^2-A[n-1]^2)/(4*A[n-2]);
%p A105745 od:
%p A105745 seq(A[i],i=1..100); # _Robert Israel_, Oct 02 2020
%t A105745 LinearRecurrence[{0,0,0,0,1},{1,12,13,4,9,9,4,5,6,8,8,6,2,4,6,4,2},100] (* or *) PadRight[{1,12,13,4,9,9,4,5,6,8,8,6},100,{4,2,2,4,6}] (* _Harvey P. Dale_, May 01 2025 *)
%Y A105745 Cf. A076839, A105736 - A105746.
%K A105745 nonn,easy
%O A105745 1,2
%A A105745 _Zak Seidov_, Apr 19 2005
%E A105745 More terms from _Robert Israel_, Oct 02 2020