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 A228879 #36 Oct 16 2024 09:00:44
%S A228879 4,7,12,21,36,63,108,189,324,567,972,1701,2916,5103,8748,15309,26244,
%T A228879 45927,78732,137781,236196,413343,708588,1240029,2125764,3720087,
%U A228879 6377292,11160261,19131876,33480783,57395628,100442349,172186884,301327047,516560652
%N A228879 a(n+2) = 3*a(n), starting 4,7.
%C A228879 Successive terms are the square roots of expressions of prior terms. The same recursive formula (see below) can be applied using any term of A001353 as the initializing value to produce the family of sequences, as given in the array A227418. This sequence uses A001353(2) = 4, and is the third row of that array.
%C A228879 a(4n) are the squares of A008776(n).
%C A228879 Binomial transform of a(n) is A021006.
%C A228879 First differences of a(n) = A083658 (without initial two terms).
%C A228879 2nd differences of a(n) = A068911 (with initial term).
%C A228879 a(n-1) is the number of n-digit base 10 numbers where all the digits are even numbers, and each digit differs by 2 from the previous and the next digit. - _Graeme McRae_, Jun 09 2014
%H A228879 Paolo Xausa, <a href="/A228879/b228879.txt">Table of n, a(n) for n = 0..1000</a>
%H A228879 Twitter / MathQuizzes, <a href="https://twitter.com/MathQuizzes/status/476017057138757633">Puzzle relating to this sequence</a>
%H A228879 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,3).
%F A228879 a(n) = sqrt(3*a(n-1)^2 + (-3)^(n-1)), a(0) = 4.
%F A228879 This divisibility relation also applies: a(n+3) = a(n+2)*a(n+1)/a(n).
%F A228879 G.f.: -(7*x+4) / (3*x^2-1). - _Colin Barker_, Jun 09 2014
%F A228879 From _Stefano Spezia_, Mar 20 2022: (Start)
%F A228879 a(n) = 3^((n-1)/2)*(4*sqrt(3) + 7 + (-1)^n*(4*sqrt(3) - 7))/2.
%F A228879 E.g.f.: 4*cosh(sqrt(3)*x) + 7*sinh(sqrt(3)*x)/sqrt(3). (End)
%t A228879 LinearRecurrence[{0, 3}, {4, 7}, 50] (* _Paolo Xausa_, Oct 14 2024 *)
%o A228879 (PARI) Vec(-(7*x+4)/(3*x^2-1) + O(x^100)) \\ _Colin Barker_, Jun 09 2014
%Y A228879 Cf. A001353, A008776, A021006, A068911, A083658, A227418.
%Y A228879 Row n = 5 of A377000.
%K A228879 nonn,easy
%O A228879 0,1
%A A228879 _Richard R. Forberg_, Sep 06 2013
%E A228879 More terms from _Colin Barker_, Jun 09 2014