Search: a106374 -id:a106374
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A005776
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Exponents m_i associated with Weyl group W(E_8).
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+10
15
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OFFSET
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1,2
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COMMENTS
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Numbers coprime to 30 in that number's reduced residue system. - Alonso del Arte, Oct 03 2017
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REFERENCES
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H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 141.
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LINKS
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MATHEMATICA
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PROG
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(Magma) Exponents(RootDatum("E8")); // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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A106403
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Primitive exponents of the Weyl group W(E_8).
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+10
5
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OFFSET
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1,1
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REFERENCES
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C. Chevalley, The Betti numbers of the exceptional Lie groups, pp. 21-24 of Proc. Internat Congress Math., Cambridge 1950, Amer. Math. Soc., 1952.
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LINKS
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FORMULA
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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A106373
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Primitive exponents of the Weyl group W(E_6).
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+10
4
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OFFSET
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1,1
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REFERENCES
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C. Chevalley, The Betti numbers of the exceptional Lie groups, pp. 21-24 of Proc. Internat Congress Math., Cambridge 1950, Amer. Math. Soc., 1952.
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LINKS
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FORMULA
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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A109161
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Triangle read by rows: T(n, k) = n*(n+9) + k + 5, with T(0, 0) = 5 and T(1, 0) = 15.
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+10
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, 95, 96, 97, 98, 99, 100, 101, 117, 118, 119, 120, 121, 122, 123, 124, 141, 142, 143, 144, 145, 146, 147, 148, 149, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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T(n, k) = n*(n+9) + k + 5, with T(0, 0) = 5 and T(1, 0) = 15.
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EXAMPLE
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Triangle begins as:
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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T[n_, k_]:= If[n==0 && k==0, 5, If[k==0 && n==1, 15, n*(n+9) +k +5]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
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PROG
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(Sage)
@CachedFunction
def T(n, k):
if (n==0 and k==0): return 5
elif (k==0 and n==1): return 15
else: return n*(n + 9) + k + 5
flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 05 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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