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 A017293 #42 Apr 04 2025 07:50:08
%S A017293 2,12,22,32,42,52,62,72,82,92,102,112,122,132,142,152,162,172,182,192,
%T A017293 202,212,222,232,242,252,262,272,282,292,302,312,322,332,342,352,362,
%U A017293 372,382,392,402,412,422,432,442,452,462,472,482,492,502,512,522,532
%N A017293 a(n) = 10*n + 2.
%C A017293 Number of 5 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (11;0) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2 and these elements are in the same relative order as those in the triple (x,y,z). In general, the number of m x n 0-1 matrices in question is given by 2^m+2m(n-1). Cf. m=2: A008574; m=3: A016933; m=4: A022144; m=6: A017569. - _Sergey Kitaev_, Nov 13 2004
%H A017293 Vincenzo Librandi, <a href="/A017293/b017293.txt">Table of n, a(n) for n = 0..5000</a>
%H A017293 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A017293 Sergey Kitaev, <a href="http://www.emis.de/journals/INTEGERS/papers/e21/e21.Abstract.html">On multi-avoidance of right angled numbered polyomino patterns</a>, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
%H A017293 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A017293 a(n) = 2*A016861(n) = A008592(n) + 2. - _Wesley Ivan Hurt_, May 03 2014
%F A017293 G.f.: 2*(1 + 4*x)/(1-x)^2. - _Vincenzo Librandi_, Jul 23 2016
%F A017293 From _Elmo R. Oliveira_, Apr 04 2025: (Start)
%F A017293 E.g.f.: 2*exp(x)*(1 + 5*x).
%F A017293 a(n) = 2*a(n-1) - a(n-2) for n >= 2.
%F A017293 a(n) = A016873(2*n). (End)
%p A017293 A017293:=n->10*n+2; seq(A017293(n), n=0..100); # _Wesley Ivan Hurt_, May 03 2014
%t A017293 Range[2, 1000, 10] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)
%t A017293 CoefficientList[Series[(2 + 8 x) / (1 - x)^2, {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 23 2016 *)
%t A017293 10 Range[0,60]+2 (* or *) LinearRecurrence[{2,-1},{2,12},60] (* _Harvey P. Dale_, Jul 04 2019 *)
%o A017293 (Magma) [10*n+2: n in [0..50]]; // _Vincenzo Librandi_, May 04 2011
%Y A017293 Subsequence of A034709, together with A017281, A139222, A139245, A017329, A139249, A139264, A139279 and A139280.
%Y A017293 Cf. A008574, A008592, A016861, A016873, A016933, A017569, A022144.
%K A017293 nonn,easy
%O A017293 0,1
%A A017293 _N. J. A. Sloane_, Dec 11 1996