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Search: id:A135912
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| A135912 |
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Number of 5-tuples (x,y,z,t,u) of nonnegative integers such that x^2+y^3+z^4+t^5+u^6 = n. |
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+0
4
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| 1, 5, 10, 10, 6, 5, 6, 4, 2, 5, 10, 10, 6, 4, 3, 1, 2, 9, 15, 11, 4, 3, 3, 1, 2, 8, 13, 12, 10, 9, 5, 2, 5, 12, 15, 9, 5, 10, 12, 6, 3, 7, 10, 9, 10, 11, 6, 2, 4, 10, 14, 10, 8, 11, 8, 2, 2, 7, 10, 9, 9, 7, 2, 2, 9, 21, 26, 16, 9, 13, 11, 3, 3, 11, 16, 12, 9, 9, 5, 3, 8, 21, 29, 21, 14, 12, 7, 3, 4
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) > 0 for n <= 10000. Is there any n for which a(n) = 0?
Note that there are many famous hard problems connected with sequences A045634, A135910, A135911 and the present entry (see the Ford reference).
The graph of this sequence suggests that a(n) is never zero. Checked to 10^5. - T. D. Noe, Mar 07 2008
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REFERENCES
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K. B. Ford, The representation of numbers as sums of unlike powers II, J. Amer. Math. Soc., 9 (1996), 919-940.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
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MAPLE
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M:=100; M2:=M^2; t0:=array(0..M2); for i from 0 to M2 do t0[i]:=0; od:
for a from 0 to M do na:=a^2; for b from 0 to M do nb:=na+b^3;
if nb <= M2 then for c from 0 to M do nc:=nb+c^4; if nc <= M2 then for d from 0 to M2 do nd:=nc+d^5; if nd <= M2 then for e from 0 to M2 do i:=nd+e^6; if i <= M2 then t0[i]:=t0[i]+1; fi; od: fi; od; fi; od: fi; od: od:
[seq(t0[i], i=0..M2)];
for i from 0 to M2 do if t0[i]=0 then lprint(i); fi; od:
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CROSSREFS
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Cf. A045634, A135910, A135911.
Sequence in context: A131891 A062986 A065755 this_sequence A040020 A123337 A038671
Adjacent sequences: A135909 A135910 A135911 this_sequence A135913 A135914 A135915
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mar 07 2008
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