

A048489


a(n) = 7 * 2^n  6.


10



1, 8, 22, 50, 106, 218, 442, 890, 1786, 3578, 7162, 14330, 28666, 57338, 114682, 229370, 458746, 917498, 1835002, 3670010, 7340026, 14680058, 29360122, 58720250, 117440506, 234881018, 469762042, 939524090, 1879048186
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OFFSET

0,2


COMMENTS

Number of 3 X n 01 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 01 matrices in question is given by 2^(m+n)2^m2^n+2.  _Sergey Kitev_, Nov 13 2004
Row sums of triangle A131115.  N. J. A. Sloane, Nov 10 2007
Equals binomial transform of [1, 7, 7, 7, ...].  Gary W. Adamson, Apr 28 2008
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 ndigit numbers produced by repeating or advancing along this 14step cycle: (0,1,2,3,4,5,6,7,6,5,4,3,2,1). Subset of A126362.  Jim Bumgardner, Dec 10 2013
a(n) = the sum of the terms in row(n) in a triangle with first column T(n,0)=
1+2*n and diagonal T(n,n)=1+4*n with T(i,j)=T(i1,j1) + T(i1,j).  J. M. Bergot, May 11 2018


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Jim Bumgardner, Variations of the Componium, 2013
S. Kitaev, On multiavoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
Index entries for linear recurrences with constant coefficients, signature (3,2).


FORMULA

a(n) = A000079(n)*76 = A005009(n)6.  Omar E. Pol, Dec 21 2008
a(n) = 2*a(n1)+6 with n>0, a(0)=1.  Vincenzo Librandi, Aug 06 2010
G.f.: ( 1+5*x ) / ( (2*x1)*(x1) ).  R. J. Mathar, Oct 21 2012
a(n) = A063757(2*n).  Philippe Deléham, Apr 13 2013


MAPLE

A048489:=n>7*2^n6: seq(A048489(n), n=0..40); # Wesley Ivan Hurt, Apr 18 2017


MATHEMATICA

CoefficientList[Series[(1 + 5 x)/((2 x  1) (x  1)), {x, 0, 28}], x] (* Michael De Vlieger, May 22 2018 *)
7*2^Range[0, 30]6 (* or *) LinearRecurrence[{3, 2}, {1, 8}, 30] (* Harvey P. Dale, May 19 2019 *)


PROG

(PARI) a(n)=7<<n6 \\ Charles R Greathouse IV, Dec 10 2013


CROSSREFS

a(n)=T(6, n), array T given by A048483.
nth difference of a(n), a(n1), ..., a(0) is (7, 7, 7, ...).
Cf. A131115.
Sequence in context: A211532 A269429 A305181 * A124701 A002968 A211530
Adjacent sequences: A048486 A048487 A048488 * A048490 A048491 A048492


KEYWORD

nonn,easy,nice


AUTHOR

Clark Kimberling


STATUS

approved



