A063130 - OEIS

%I #15 Aug 22 2019 12:18:12

%S 7,22,38,54,70,86,102,118,134,150,166,182,198,214,230,246,262,278,294,

%T 310,326,342,358,374,390,406,422,438,454,470,486,502,518,534,550,566,

%U 582,598,614,630,646,662,678,694,710,726,742,758,774,790

%N Dimension of the space of weight 2n cusp forms for Gamma_0( 62 ).

%C 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

%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 William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>.

%H William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>

%F Conjectures from _Colin Barker_, Jun 13 2016: (Start)

%F a(n) = 2*(8*n-5) for n>1.

%F a(n) = 2*a(n-1)-a(n-2) for n>3.

%F G.f.: x*(1+x)*(7+x) / (1-x)^2.

%F (End)

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jul 08 2001