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 A069396 #15 May 09 2023 06:43:44
%S A069396 1,25,377,4541,48329,476389,4461489,40306317,354713977,3060942133,
%T A069396 26020259201,218626028573,1820140085705,15043088032837,
%U A069396 123602247055953,1010793162739629,8234370308667673,66870924588036181
%N A069396 Half the number of 3 X n binary arrays with a path of adjacent 1's and a path of adjacent 0's from top row to bottom row.
%H A069396 G. C. Greubel, <a href="/A069396/b069396.txt">Table of n, a(n) for n = 2..1000</a>
%F A069396 G.f.: x^2*(2*x+1)^2/(1-8*x)/(2*x^2-7*x+1)/(4*x^2-6*x+1). - _Vladeta Jovovic_, Jul 02 2003
%F A069396 2*a(n) = 8^n+A084326(n+1) -2*A186446(n). - _R. J. Mathar_, May 09 2023
%t A069396 Drop[CoefficientList[Series[x^2*(2*x+1)^2/(1-8*x)/(2*x^2-7*x + 1)/(4*x^2 - 6*x + 1), {x, 0, 50}], x], 2] (* _G. C. Greubel_, Apr 22 2018 *)
%o A069396 (PARI) x='x+O('x^30); Vec(x^2*(2*x+1)^2/(1-8*x)/(2*x^2-7*x+1)/(4*x^2 -6*x+1)) \\ _G. C. Greubel_, Apr 22 2018
%o A069396 (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x^2*(2*x+1)^2/(1-8*x)/(2*x^2-7*x+1)/(4*x^2-6*x+1))); // _G. C. Greubel_, Apr 22 2018
%Y A069396 Cf. 1 X n A000225, 2 X n A016269, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.
%K A069396 nonn
%O A069396 2,2
%A A069396 _R. H. Hardin_, Mar 22 2002