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%I #85 Sep 08 2022 08:44:36
%S 0,10,20,30,40,50,60,70,80,90,100,110,120,130,140,150,160,170,180,190,
%T 200,210,220,230,240,250,260,270,280,290,300,310,320,330,340,350,360,
%U 370,380,390,400,410,420,430,440,450,460,470,480,490,500,510,520,530
%N Multiples of 10: a(n) = 10 * n.
%C Number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01,1) and (11;0). 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 (n+2)*2^(m-1)+2*m*(n-1)-2 for m>1 and n>1. - _Sergey Kitaev_, Nov 12 2004
%C If Y is a 5-subset of an n-set X then, for n>=5, a(n-4) is the number of 3-subsets of X having at least two elements in common with Y. - _Milan Janjic_, Dec 08 2007
%C Complement of A067251; A168184(a(n)) = 0. [_Reinhard Zumkeller_, Nov 30 2009]
%C Where record values occur for the number of partitions of n into powers of 10: A179052(n) = A179051(a(n)). [_Reinhard Zumkeller_, Jun 27 2010]
%C Numbers ending in 0. - _Wesley Ivan Hurt_, Apr 10 2016
%H Ivan Panchenko, <a href="/A008592/b008592.txt">Table of n, a(n) for n = 0..200</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=322">Encyclopedia of Combinatorial Structures 322</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 Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F From _Vincenzo Librandi_, Dec 24 2010: (Start)
%F G.f.: 10*x/(x-1)^2.
%F a(n) = 2*a(n-1)-a(n-2) for n>1. (End)
%F a(n) = Sum_{i=2n-2..2n+2} i. - _Wesley Ivan Hurt_, Apr 11 2016
%F E.g.f.: 10*x*exp(x). - _Stefano Spezia_, May 31 2021
%p A008592:=n->10*n: seq(A008592(n), n=0..100); # _Wesley Ivan Hurt_, Apr 10 2016
%t Range[0, 1000, 10] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)
%o (Haskell) a008592 = (10 *) -- _Reinhard Zumkeller_, Jun 13 2015
%o (PARI) vector(50, n, n--; 10*n) \\ _Michel Marcus_, Feb 05 2016
%o (PARI) x='x+O('x^999); concat(0, Vec(10*x/(x-1)^2)) \\ _Altug Alkan_, Apr 11 2016
%o (PARI) apply( A008592(n)=10*n, [1..55]) \\ _M. F. Hasler_, Apr 23 2021
%o (Magma) [10*n : n in [0..100]]; // _Wesley Ivan Hurt_, Apr 10 2016
%Y Cf. A008590, A008591, A067251, A168184, A179051, A179052.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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