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%I #43 Sep 08 2022 08:44:42
%S 6,16,26,36,46,56,66,76,86,96,106,116,126,136,146,156,166,176,186,196,
%T 206,216,226,236,246,256,266,276,286,296,306,316,326,336,346,356,366,
%U 376,386,396,406,416,426,436,446,456,466,476,486,496,506,516,526,536
%N a(n) = 10*n + 6.
%C Number of 4 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) 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 same relative order as those in the triple (x,y,z). - _Sergey Kitaev_, Nov 11 2004
%C Numbers k such that k and (4^h)^k end with the same digit, where h > 0. - _Bruno Berselli_, Dec 13 2018
%H Vincenzo Librandi, <a href="/A017341/b017341.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 S. Kitaev, <a href="https://web.archive.org/web/20130625171839/http://www.ms.uky.edu/~math/MAreport/4-ser.ps">On multi-avoidance of right angled numbered polyomino patterns</a>, University of Kentucky Research Reports (2004).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 2*a(n-1) - a(n-2) with n>1, a(0)=6, a(1)=16. - _Vincenzo Librandi_, May 29 2011
%F a(n) = (n+1)*A016861(n+1) - n*A016861(n). - _Bruno Berselli_, Jan 18 2013
%F From _Stefano Spezia_, May 31 2021: (Start)
%F G.f.: 2*(3 + 2*x)/(1 - x)^2.
%F E.g.f.: 2*(3 + 5*x)*exp(x). (End)
%t Range[6, 1000, 10] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)
%o (Magma) [10*n+6: n in [0..60]]; // _Vincenzo Librandi_, May 29 2011
%o (PARI) a(n)=10*n+6 \\ _Charles R Greathouse IV_, Jul 10 2016
%Y Cf. A008592, A016861, A017329.
%Y Cf. A000400 (powers of 6).
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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