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%I #37 Sep 08 2022 08:44:42
%S 2,12,22,32,42,52,62,72,82,92,102,112,122,132,142,152,162,172,182,192,
%T 202,212,222,232,242,252,262,272,282,292,302,312,322,332,342,352,362,
%U 372,382,392,402,412,422,432,442,452,462,472,482,492,502,512,522,532
%N a(n) = 10n+2.
%C 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 Vincenzo Librandi, <a href="/A017293/b017293.txt">Table of n, a(n) for n = 0..5000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H S. 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).
%F a(n) = 2 * A016861(n) = A008592(n) + 2. - _Wesley Ivan Hurt_, May 03 2014
%F G.f.: 2*(1 + 4*x)/(1-x)^2. - _Vincenzo Librandi_, Jul 23 2016
%p A017293:=n->10*n+2; seq(A017293(n), n=0..100); # _Wesley Ivan Hurt_, May 03 2014
%t Range[2, 1000, 10] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)
%t CoefficientList[Series[(2 + 8 x) / (1 - x)^2, {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 23 2016 *)
%t 10 Range[0,60]+2 (* or *) LinearRecurrence[{2,-1},{2,12},60] (* _Harvey P. Dale_, Jul 04 2019 *)
%o (Magma) [10*n+2: n in [0..50]]; // _Vincenzo Librandi_, May 04 2011
%Y Subsequence of A034709, together with A017281, A139222, A139245, A017329, A139249, A139264, A139279 and A139280.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Dec 11 1996
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