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Search: id:A109161
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| A109161 |
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n: R^n real coefficient for exceptional Cartan groups as a triangular sequence: G2->R^5; F4->R^15; E6->R^16; E7->R^27; E7.5->R^28; E8->R^29; ... |
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+0
3
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| 5, 15, 16, 27, 28, 29, 41, 42, 43, 44, 57, 58, 59, 60, 61, 75, 76, 77, 78, 79, 80
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Even though the sequence itself isn't controversial as a numerical function, the interpretation that there are higher exceptional groups may well be. In that matter I make no firm claim, just a conjecture.
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LINKS
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S. Helgason, A Centennial: Wilhelm Killing and the Exceptional Groups, Mathematical Intelligencer 12, no. 3 (1990). [See p. 3.]
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FORMULA
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t(n,m) =If[n == 0 && m == 0, 5, If[n == 0 && m == 1, 15, 5 + (m)*(10 + m - 1) + n]]
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EXAMPLE
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{5},
{15, 16},
{27, 28, 29},
{41, 42, 43, 44},
{57, 58, 59, 60, 61},
{75, 76, 77, 78, 79, 80}
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MATHEMATICA
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f[n_, m_] = If[n == 0 && m == 0, 5, If[n == 0 && m == 1, 15, 5 + (m)*(10 + m - 1) + n]]; a = Table[Table[f[n, m], {n, 0, m}], {m, 0, 5}]; Flatten[a]
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CROSSREFS
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Cf. A106373, A106374, A106403.
Sequence in context: A102185 A030486 A101238 this_sequence A065908 A134453 A022417
Adjacent sequences: A109158 A109159 A109160 this_sequence A109162 A109163 A109164
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), May 06 2007
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