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 A048489 #69 May 19 2019 09:10:47
%S A048489 1,8,22,50,106,218,442,890,1786,3578,7162,14330,28666,57338,114682,
%T A048489 229370,458746,917498,1835002,3670010,7340026,14680058,29360122,
%U A048489 58720250,117440506,234881018,469762042,939524090,1879048186
%N A048489 a(n) = 7 * 2^n - 6.
%C A048489 Number of 3 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (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 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+n)-2^m-2^n+2. - _Sergey Kitev_, Nov 13 2004
%C A048489 Row sums of triangle A131115. - _N. J. A. Sloane_, Nov 10 2007
%C A048489 Equals binomial transform of [1, 7, 7, 7, ...]. - _Gary W. Adamson_, Apr 28 2008
%C A048489 Number of variations of a Componium barrel which produces n phrases. This sequence describes the variations produced by the Componium, a historical mechanical organ. Another way of describing it is: Number of base 8 n-digit numbers produced by repeating or advancing along this 14-step cycle: (0,1,2,3,4,5,6,7,6,5,4,3,2,1). Subset of A126362. - _Jim Bumgardner_, Dec 10 2013
%C A048489 a(n) = the sum of the terms in row(n) in a triangle with first column T(n,0)=
%C A048489 1+2*n and diagonal T(n,n)=1+4*n with T(i,j)=T(i-1,j-1) + T(i-1,j). - _J. M. Bergot_, May 11 2018
%H A048489 Vincenzo Librandi, <a href="/A048489/b048489.txt">Table of n, a(n) for n = 0..1000</a>
%H A048489 Jim Bumgardner, <a href="http://jbum.com/papers/componium_variations.pdf">Variations of the Componium</a>, 2013
%H A048489 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 A048489 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A048489 a(n) = A000079(n)*7-6 = A005009(n)-6. - _Omar E. Pol_, Dec 21 2008
%F A048489 a(n) = 2*a(n-1)+6 with n>0, a(0)=1. - _Vincenzo Librandi_, Aug 06 2010
%F A048489 G.f.: ( 1+5*x ) / ( (2*x-1)*(x-1) ). - _R. J. Mathar_, Oct 21 2012
%F A048489 a(n) = A063757(2*n). - _Philippe Deléham_, Apr 13 2013
%p A048489 A048489:=n->7*2^n-6: seq(A048489(n), n=0..40); # _Wesley Ivan Hurt_, Apr 18 2017
%t A048489 CoefficientList[Series[(1 + 5 x)/((2 x - 1) (x - 1)), {x, 0, 28}], x] (* _Michael De Vlieger_, May 22 2018 *)
%t A048489 7*2^Range[0,30]-6 (* or *) LinearRecurrence[{3,-2},{1,8},30] (* _Harvey P. Dale_, May 19 2019 *)
%o A048489 (PARI) a(n)=7<<n-6 \\ _Charles R Greathouse IV_, Dec 10 2013
%Y A048489 a(n)=T(6, n), array T given by A048483.
%Y A048489 n-th difference of a(n), a(n-1), ..., a(0) is (7, 7, 7, ...).
%Y A048489 Cf. A131115.
%K A048489 nonn,easy,nice
%O A048489 0,2
%A A048489 _Clark Kimberling_