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A063116
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Dimension of the space of weight 2n cusp forms for Gamma_0( 48 ).
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0
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3, 18, 34, 50, 66, 82, 98, 114, 130, 146, 162, 178, 194, 210, 226, 242, 258, 274, 290, 306, 322, 338, 354, 370, 386, 402, 418, 434, 450, 466, 482, 498, 514, 530, 546, 562, 578, 594, 610, 626, 642, 658, 674, 690, 706, 722, 738, 754, 770, 786
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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G.f.: x*(3 + 12*x + x^2) / (1 - x)^2.
a(n) = 2*a(n-1) - a(n-2) for n>3.
a(n) = 2*(8*n-7) for n>1.
(End)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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