A063130 Dimension of the space of weight 2n cusp forms for Gamma_0( 62 ).

7, 22, 38, 54, 70, 86, 102, 118, 134, 150, 166, 182, 198, 214, 230, 246, 262, 278, 294, 310, 326, 342, 358, 374, 390, 406, 422, 438, 454, 470, 486, 502, 518, 534, 550, 566, 582, 598, 614, 630, 646, 662, 678, 694, 710, 726, 742, 758, 774, 790

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

Table of n, a(n) for n=1..50.

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

Sequence in context: A161447 A047718 A031053 * A275642 A171441 A341401

Adjacent sequences: A063127 A063128 A063129 * A063131 A063132 A063133

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2001

Status

approved