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Search: id:A072945
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| A072945 |
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Number of numbers of the form x^3+y^2+x*y less than or equal to n (x,y >=0). |
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+0
1
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| 1, 3, 3, 4, 5, 5, 5, 6, 7, 8, 8, 9, 9, 10, 10, 10, 12, 12, 12, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 18, 19, 19, 19, 19, 20, 21, 21, 21, 21, 21, 21, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 26, 27, 28, 28, 28, 28, 28, 28, 28, 30, 30, 30, 31, 31, 32, 32, 33, 33
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Using Ikehara's theorem one can show that a(n) is asymptotic to C*n^(5/6) where C is a positive constant >0.7
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EXAMPLE
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0^3 + 0^2 + 0*0, 0^3 + 1^2 + 0*1, 1^3 + 0^2 + 1*0 are 3 numbers <= 1 hence a(1) = 3.
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PROGRAM
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(PARI) a(n)=sum(i=0, n, sum(j=0, n, if((sign(i^3+j^2+i*j-n)+1)*sign(i^3+j^2+i*j-n), 0, 1)))
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CROSSREFS
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Adjacent sequences: A072942 A072943 A072944 this_sequence A072946 A072947 A072948
Sequence in context: A108216 A064631 A072648 this_sequence A120180 A063197 A011977
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 14 2002
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