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 A213763 #23 Feb 17 2024 14:30:46
%S A213763 1,11,43,127,331,807,1891,4319,9691,21463,47059,102351,221131,475079,
%T A213763 1015747,2162623,4587451,9699255,20447155,42991535,90177451,188743591,
%U A213763 394264483,822083487,1711275931,3556769687,7381974931
%N A213763 Principal diagonal of the convolution array A213762.
%C A213763 Create a triangle with first column T(n,1)=1+4*n for n=0,1,2... The remaining terms T(r,c)=T(r,c-1)+T(r-1,c-1). The sum of the terms in row(n)=a(n+1). - _J. M. Bergot_, Dec 18 2012
%H A213763 Clark Kimberling, <a href="/A213763/b213763.txt">Table of n, a(n) for n = 1..1000</a>
%H A213763 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,12,-4).
%F A213763 a(n) = -1 + 2^n - 4*n + n*2^(n+1).
%F A213763 a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4).
%F A213763 G.f.: x*(1 + 5*x - 10*x^2)/(1 - 3*x + 2*x^2 )^2.
%t A213763 (See A213762.)
%t A213763 LinearRecurrence[{6,-13,12,-4},{1,11,43,127},30] (* _Harvey P. Dale_, Apr 13 2017 *)
%Y A213763 Cf. A213762, A213500.
%K A213763 nonn,easy
%O A213763 1,2
%A A213763 _Clark Kimberling_, Jun 20 2012