# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a063116
Showing 1-1 of 1

%I A063116 #24 Sep 12 2019 12:33:29
%S A063116 3,18,34,50,66,82,98,114,130,146,162,178,194,210,226,242,258,274,290,
%T A063116 306,322,338,354,370,386,402,418,434,450,466,482,498,514,530,546,562,
%U A063116 578,594,610,626,642,658,674,690,706,722,738,754,770,786
%N A063116 Dimension of the space of weight 2n cusp forms for Gamma_0( 48 ).
%C A063116 Conjecture: For n>=2, a(n) is the difference between the greater of successive pairs of odd triangular numbers(A000217), namely A(B(n-1)+1) - A(B(n-2)+1), where A=A000217 and B=A016813. This reduces to a(n)=2*(8*n-7) (see Formula). (1,3),(15,21) are the first consecutive pairs of odd triangular numbers, and 21-3=18, which is a(2). - _David James Sycamore_, Sep 12 2019
%H A063116 William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>.
%H A063116 William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>
%F A063116 Conjectures from _Colin Barker_, Jun 09 2019: (Start)
%F A063116 G.f.: x*(3 + 12*x + x^2) / (1 - x)^2.
%F A063116 a(n) = 2*a(n-1) - a(n-2) for n>3.
%F A063116 a(n) = 2*(8*n-7) for n>1.
%F A063116 (End)
%Y A063116 Cf. A016813, A000217.
%K A063116 nonn
%O A063116 1,1
%A A063116 _N. J. A. Sloane_, Jul 08 2001

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE