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Search: id:A164283
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| A164283 |
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Number of ways to write n as the root-mean-square (RMS) of a set of distinct positive integers. |
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+0
1
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| 1, 1, 1, 1, 3, 9, 19, 79, 225, 693, 1901, 5597, 17641, 57503, 195431, 647139, 2182987, 7344451, 25057681, 85742999, 295284367, 1028155825, 3596134963, 12659796475, 44696280143, 158226554179, 562623263251, 2006471222195, 7182910999719
(list; graph; listen)
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OFFSET
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1,5
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LINKS
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Eric Weisstein's World of Math, Root-Mean-Square
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EXAMPLE
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a(6) = 9, because 6 is the RMS of 9 sets of distinct positive integers: 6 = RMS(6) = RMS(1,3,5,8,9) = RMS(3,4,5,7,9) = RMS(1,2,4,5,7,11) = RMS(1,3,5,6,8,9) = RMS(3,4,5,6,7,9) = RMS(1,2,3,5,7,8,10) = RMS(1,2,4,5,6,7,11) = RMS(1,2,3,5,6,7,8,10).
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MAPLE
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sns:= proc(i) option remember; `if` (i=1, 1, sns(i-1) +i^2) end: b:= proc(n, i, t) if n<0 or i<t then 0 elif n=0 then `if` (t=0, 1, 0) elif i=1 then `if` (n=1 and t=1, 1, 0) else b(n, i, t):= b(n, i-1, t) +b(n-i^2, i-1, t-1) fi end: a:= proc(n) option remember; local s, k; s:= 1; for k from 2 while sns(k)<=k*n^2 do s:= s +b(k*n^2, floor (sqrt (k*n^2 -sns(k-1))), k) od; s end: seq (a(n), n=1..15);
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CROSSREFS
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Cf. A163974, A066572, A066571, A072701.
Sequence in context: A130586 A147146 A146066 this_sequence A033315 A073716 A037048
Adjacent sequences: A164280 A164281 A164282 this_sequence A164284 A164285 A164286
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 12 2009
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