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 A168314 #11 Aug 28 2024 09:36:40
%S A168314 1,1,3,5,13,29,71,165,401,957,2315,5561,13437,32377,78191,188617,
%T A168314 455425,1099137,2653699,6405733,15465165,37334149,90133463,217596445,
%U A168314 525326353,1268238029,3061802411,7391815977,17845434365,43082619953,104010674271,251103812113
%N A168314 Eigensequence of triangle A168313.
%C A168314 Conjectured convergent of a(n)/a(n-1) = (1+sqrt(2)). E.g.: a(19)/a(18) = 2653699/1099137 = 2.4143478...
%F A168314 Equals the eigensequence of triangle A168313 = lim_{n->oo} M^n where M = A168313 shifted down one row and inserting a "1" at top.
%F A168314 Equals the left column vector as a sequence.
%o A168314 (Python)
%o A168314 a = [1]
%o A168314 for n in range(30):
%o A168314 a.append(2*sum(a[n//2:-1]) + a[-1])
%o A168314 print(a) # _Andrey Zabolotskiy_, Aug 28 2024
%Y A168314 Cf. A168313, A168315.
%K A168314 eigen,nonn
%O A168314 1,3
%A A168314 _Gary W. Adamson_, Nov 22 2009
%E A168314 Terms a(20) and beyond from _Andrey Zabolotskiy_, Aug 28 2024