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 A069306 #32 Jul 19 2024 19:06:15
%S A069306 5,12,29,70,169,408,985,2378,5741,13860,33461,80782,195025,470832,
%T A069306 1136689,2744210,6625109,15994428,38613965,93222358,225058681,
%U A069306 543339720,1311738121,3166815962,7645370045,18457556052,44560482149,107578520350,259717522849,627013566048,1513744654945,3654502875938
%N A069306 Number of 2 X n binary arrays with a path of adjacent 1's from upper left corner to anywhere in right hand column.
%H A069306 Indranil Ghosh, <a href="/A069306/b069306.txt">Table of n, a(n) for n = 2..2607</a>
%H A069306 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A069306 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,1).
%F A069306 G.f.: x^2(2x+5)/(1-2x-x^2). a(n) = A000129(n+1), as proved by Tomislav Doslic. - _Ralf Stephan_, Nov 16 2004
%F A069306 a(n) = 2*a(n-1)+a(n-2). [_Philippe Deléham_, Nov 20 2008]
%t A069306 LinearRecurrence[{2, 1}, {5, 12}, 50] (* _Paolo Xausa_, Jul 19 2024 *)
%Y A069306 Cf. A069307 (3 X n), A069308 (4 X n), A069309 (5 X n), A069310 (6 X n), A069311 (7 X n), A069312 (8 X n), A069313 (9 X n), A069314 (10 X n), A069315 (11 X n), A069316 (12 X n), A069317 (13 X n), A069318 (14 X n), A069319 (15 X n), A069320 (16 X n).
%Y A069306 Cf. A069294-A069305 (by columns).
%Y A069306 Cf. A000129, A048624, A077985.
%K A069306 nonn,easy
%O A069306 2,1
%A A069306 _R. H. Hardin_, Mar 14 2002