OFFSET
1,1
COMMENTS
Number of 4 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
LINKS
S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
William A. Stein, The modular forms database
FORMULA
Conjectures from Colin Barker, Jun 13 2016: (Start)
a(n) = 2*(8*n-5) for n>1.
a(n) = 2*a(n-1)-a(n-2) for n>3.
G.f.: x*(1+x)*(7+x) / (1-x)^2.
(End)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 08 2001
STATUS
approved