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Search: id:A061790
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| A061790 |
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Number of sums i^2 + j^2 that occur more than once for 1<=i<=j<=n. |
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1
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| 0, 0, 0, 0, 0, 0, 1, 2, 3, 3, 5, 6, 8, 11, 12, 14, 18, 20, 25, 27, 31, 35, 42, 46, 50, 55, 61, 67, 74, 78, 87, 94, 101, 111, 118, 124, 133, 143, 153, 159, 172, 181, 193, 206, 214, 227, 240, 251, 265, 277, 290, 303, 322, 337, 350, 363, 378, 392, 410, 421, 440, 461
(list; graph; listen)
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OFFSET
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1,8
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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,...,100,121} provides 61 different sums of two, not necessarily different squares: {2,5,8,..,202,221,242}. Only 5 sums arise more than once: 50=1+49=25+25;65=1+64=16+49;85=4+81=36+49; 125=4+121=25+100;130=9+121=49+81. Therefore a(11)=(12*11/2)-61=5.
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MATHEMATICA
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f[x_] := x^2 t0=Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, {u, 1, m}]]]], {m, 1, 75}] t1=Table[(w*(w+1)/2)-Part[t0, w], {w, a, b}]
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CROSSREFS
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A000217.
Sequence in context: A039852 A035938 A024503 this_sequence A107236 A027586 A039860
Adjacent sequences: A061787 A061788 A061789 this_sequence A061791 A061792 A061793
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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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