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Search: id:A061786
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| A061786 |
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Number of distinct sums i^2 + j^2 for 1<=i<=j<=n. |
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+0
4
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| 1, 3, 6, 10, 15, 21, 27, 34, 42, 52, 61, 72, 83, 94, 108, 122, 135, 151, 165, 183, 200, 218, 234, 254, 275, 296, 317, 339, 361, 387, 409, 434, 460, 484, 512, 542, 570, 598, 627, 661, 689, 722, 753, 784, 821, 854, 888, 925, 960, 998, 1036, 1075, 1109, 1148
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OFFSET
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1,2
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EXAMPLE
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If the {s+t} sums are generated by addition 2 terms of an S set consisting of n different entries, then at least 1, at most n(n+1)/2=A000217(n) distinct values can be obtained. The set of first n squares gives results falling between these two extremes. E.g. S={1,4,9,16,25,36,49} provides 27 different sums of two, not necessarily different squares: {2,5,8,10,13,17,18,20,25,26,29,32,34,37,40,41,45,50,52,53,58,61,65,72,74,85,98}_ Only a single sum arises more than once: 50=1+49=25+25. Therefore a(7)=(7*8/2)-1=27.
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MATHEMATICA
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f[x_] := x^2 Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, {u, 1, m}]]]], {m, 1, 75}]
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CROSSREFS
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A000217.
Sequence in context: A115015 A056150 A033439 this_sequence A105334 A130486 A054636
Adjacent sequences: A061783 A061784 A061785 this_sequence A061787 A061788 A061789
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 22 2001
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