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Search: id:A061035
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| A061035 |
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Triangle T(m,n) = numerator of 1/m^2 - 1/n^2, n >= 1, m=n,n-1,n-2,...,1. |
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+0
12
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| 0, 0, 3, 0, 5, 8, 0, 7, 3, 15, 0, 9, 16, 21, 24, 0, 11, 5, 1, 2, 35, 0, 13, 24, 33, 40, 45, 48, 0, 15, 7, 39, 3, 55, 15, 63, 0, 17, 32, 5, 56, 65, 8, 77, 80, 0, 19, 9, 51, 4, 3, 21, 91, 6, 99, 0, 21, 40, 57, 72, 85, 96, 105, 112, 117, 120, 0, 23, 11, 7, 5, 95, 1, 119, 1, 5, 35, 143, 0
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Wavelengths in hydrogen spectrum are given by Rydberg's formula 1/wavelength = constant*(1/m^2 - 1/n^2).
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REFERENCES
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J. E. Brady and G. E. Humiston, General Chemistry, 3rd. ed., Wiley; p. 77.
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LINKS
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J. J. O'Connor and E. F. Robertson, Johannes Robert Rydberg
Eric Weisstein's World of Physics, Balmer Formula
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EXAMPLE
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Triangle 1/m^2-1/n^2, m >= 1, 1<=n<=m, (i.e. with rows reversed) begins
0
3/4, 0
8/9, 5/36, 0
15/16, 3/16, 7/144, 0
24/25, 21/100, 16/225, 9/400, 0
35/36, 2/9, 1/12, 5/144, 11/900, 0
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CROSSREFS
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Cf. A061036. Rows give A061037-A061050.
Sequence in context: A052483 A019915 A052123 this_sequence A021331 A013673 A103229
Adjacent sequences: A061032 A061033 A061034 this_sequence A061036 A061037 A061038
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KEYWORD
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nonn,tabl,easy,nice,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), May 26 2001
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EXTENSIONS
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More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jul 15 2001
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