

A109161


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; ...


2



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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OFFSET

1,1


COMMENTS

Even though the sequence itself is not 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.


LINKS

Table of n, a(n) for n=1..21.
S. Helgason, A Centennial: Wilhelm Killing and the Exceptional Groups, Mathematical Intelligencer 12, no. 3 (1990). [See p. 3.]


FORMULA

t(n,m) =If[n == 0 && m == 0, 5, If[n == 0 && m == 1, 15, 5 + (m)*(10 + m  1) + n]]


EXAMPLE

{5},
{15, 16},
{27, 28, 29},
{41, 42, 43, 44},
{57, 58, 59, 60, 61},
{75, 76, 77, 78, 79, 80}


MATHEMATICA

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]


CROSSREFS

Cf. A106373, A106374, A106403.
Sequence in context: A102185 A030486 A101238 * A065908 A297124 A166503
Adjacent sequences: A109158 A109159 A109160 * A109162 A109163 A109164


KEYWORD

nonn,tabl,uned


AUTHOR

Roger L. Bagula, May 06 2007


STATUS

approved



