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 A047860 #30 Sep 08 2022 08:44:57
%S A047860 1,5,14,34,78,174,382,830,1790,3838,8190,17406,36862,77822,163838,
%T A047860 344062,720894,1507326,3145726,6553598,13631486,28311550,58720254,
%U A047860 121634814,251658238,520093694,1073741822,2214592510,4563402750
%N A047860 a(n) = T(3,n), array T given by A047858.
%C A047860 The Wikipedia article on L-system Example 2 is "Pythagoras Tree" given by the axiom: 0 and rules: 1 -> 11, 0 -> 1[0]0. The length of the n-th string of symbols is a(n). This interpretation leads to a matrix power formula for a(n). - _Michael Somos_, Jan 12 2015
%H A047860 Vincenzo Librandi, <a href="/A047860/b047860.txt">Table of n, a(n) for n = 0..3000</a>
%H A047860 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).
%H A047860 Wikipedia, <a href="http://en.wikipedia.org/wiki/L-system#Example_2:_Pythagoras_Tree">L-system</a> Example 2: Pythagoras Tree
%F A047860 Main diagonal of the array defined by T(0, j)=j+1 j>=0, T(i, 0)=i+1 i>=0, T(i, j)=T(i-1, j-1)+T(i-1, j)+ 2; a(n)=2^(n-1)*(n+6)-2. - _Benoit Cloitre_, Jun 17 2003
%F A047860 a(0)=1, a(1)=5, a(2)=14, a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3). - _Vincenzo Librandi_, Sep 28 2011
%e A047860 G.f. = 1 + 5*x + 14*x^2 + 34*x^3 + 78*x^4 + 174*x^5 + 382*x^6 + 830*x^7 + ...
%e A047860 Using the Pythagoras Tree L-system, a(0) = #0 = 1, a(1) = #1[0]0 = 5, a(2) = #11[1[0]0]1[0]0 = 14. - _Michael Somos_, Jan 12 2015
%t A047860 LinearRecurrence[{5,-8,4},{1,5,14},30] (* _Harvey P. Dale_, Sep 29 2012 *)
%o A047860 (Magma) [2^(n-1)*(n+6)-2: n in [0..30]]; // _Vincenzo Librandi_, Sep 28 2011
%o A047860 (PARI) {a(n) = if( n<0, 0, [1, 1, 1, 1] * [2, 0, 0, 0; 1, 2, 0, 0; 1, 0, 1, 0; 1, 0, 0, 1]^n * [1, 0, 0, 0]~ )}; /* _Michael Somos_, Jan 12 2015 */
%o A047860 (PARI) a(n)=([0,1,0; 0,0,1; 4,-8,5]^n*[1;5;14])[1,1] \\ _Charles R Greathouse IV_, Jul 19 2016
%Y A047860 n-th difference of a(n), a(n-1), ..., a(0) is (4, 5, 6, ...).
%Y A047860 First differences of A027993.
%K A047860 nonn,easy
%O A047860 0,2
%A A047860 _Clark Kimberling_