OFFSET
0,2
COMMENTS
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
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 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
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(i-1,j-1) + T(i-1,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 multi-avoidance 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) = 2*a(n-1)+6 with n>0, a(0)=1. - Vincenzo Librandi, Aug 06 2010
G.f.: ( 1+5*x ) / ( (2*x-1)*(x-1) ). - R. J. Mathar, Oct 21 2012
a(n) = A063757(2*n). - Philippe Deléham, Apr 13 2013
MAPLE
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<<n-6 \\ Charles R Greathouse IV, Dec 10 2013
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved