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 A069362 #25 Jan 07 2023 12:26:57
%S A069362 1,41,1041,22193,433809,8057905,144769425,2541013617,43843180113,
%T A069362 746691527217,12588144461329,210502738714097,3497001564166609,
%U A069362 57781030561348017,950437243856526737,15574913193760097649,254416775893204873553,4144677558181255455025
%N A069362 Number of 4 X n binary arrays with a path of adjacent 1's from top row to bottom row.
%H A069362 Colin Barker, <a href="/A069362/b069362.txt">Table of n, a(n) for n = 1..800</a>
%H A069362 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (35,-378,1264,-1272,-128).
%F A069362 G.f.: x*(1 +6*x -16*x^2 -8*x^3)/((1 -16*x)*(1 -19*x +74*x^2 -80*x^3 - 8*x^4)).
%t A069362 Rest[CoefficientList[Series[x*(1+6*x-16*x^2-8*x^3)/((1-16*x)*(1-19*x+ 74*x^2 -80*x^3-8*x^4)), {x,0,50}],x]] (* _G. C. Greubel_, Apr 22 2018 *)
%t A069362 LinearRecurrence[{35,-378,1264,-1272,-128},{1,41,1041,22193,433809},20] (* _Harvey P. Dale_, Jan 01 2019 *)
%o A069362 (PARI) Vec(x*(1 + 6*x - 16*x^2 - 8*x^3) / ((1 - 16*x)*(1 - 19*x + 74*x^2 - 80*x^3 - 8*x^4)) + O(x^30)) \\ _Colin Barker_, Oct 12 2017
%o A069362 (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+6*x-16*x^2-8*x^3)/((1-16*x)*(1-19*x+ 74*x^2 -80*x^3-8*x^4)))); // _G. C. Greubel_, Apr 22 2018
%Y A069362 Row 4 of A359576.
%Y A069362 Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, 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 A069362 nonn,easy
%O A069362 1,2
%A A069362 _R. H. Hardin_, Mar 22 2002