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Search: id:A084231
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| A084231 |
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Numbers n such that root-mean-square value of 1, 2, ..., n, sqrt(Sum(k^2, k, 1, n)/n), is an integer. |
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+0
2
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| 1, 337, 65521, 12710881, 2465845537, 478361323441, 92799630902161, 18002650033695937, 3492421306906109761, 677511730889751597841, 131433783371304903871537, 25497476462302261599480481
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Equivalently, sqrt((n+1)*(2*n+1)/6) is an integer.
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n)=((7/2 + 2sqrt(3))(97 + 56sqrt(3))^n + (7/2 - 2sqrt(3))(97 - 56sqrt(3))^n - 3)/4 a(n)=([(7/2 + 2sqrt(3))(97 + 56rq(3))^n] - 2)/4, [x] = integer part of x. a(n+3)=195(a(n+2) - a(n+1)) + a(n).
G.f.: x(1+142x+x^2)/[(1-x)(1-194x+x^2)].
a(n)=((7-4sqrt(3))^(1+2n)+(7+4sqrt(3))^(1+2n)-6)/8. - Peter Pein (peter.pein(AT)dordos.de), Mar 03 2005
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EXAMPLE
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a(1)=337 because sqrt(Sum(k^2, k, 1, 337)/337) is integer (195=A084232(1))
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MATHEMATICA
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a[n_]:=Expand[((7-4Sqrt[3])^(1+2n)+(7+4Sqrt[3])^(1+2n)-6)/8] (Pein)
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CROSSREFS
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Cf. A084232.
Sequence in context: A020358 A051962 A142830 this_sequence A066478 A031128 A070311
Adjacent sequences: A084228 A084229 A084230 this_sequence A084232 A084233 A084234
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KEYWORD
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nonn
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AUTHOR
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Ignacio Larrosa Canestro (ilarrosa(AT)mundo-r.com), May 20 2003
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EXTENSIONS
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One more term from Peter Pein (peter.pein(AT)dordos.de), Mar 03 2005
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