A129844 Triangular sequence constructed from heights of irreducible representations of semi-simple Lie algebras (groups A1, G2, F4, E6, E7, E8).

1, 6, 10, 16, 22, 30, 42, 16, 16, 22, 30, 30, 42, 27, 34, 49, 52, 66, 75, 96, 58, 92, 114, 136, 168, 182, 220, 270

Offset

1,2

References

R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Dover, NY, 2006, ISBN 0-486-44999-8, p. 139.

E. B. Dynkin, Semisimple subalgebras of semisimple Lie algebras, Amer. Math. Soc. Translations, Vol. 6, 1957, pages 111-244.

Links

Table of n, a(n) for n=1..28.

Example

Triangle begins:
  {1},
  {6, 10},
  {16, 22, 30, 42},
  {16, 16, 22, 30, 30, 42},
  {27, 34, 49, 52, 66, 75, 96},
  {58, 92, 114, 136, 168, 182, 220, 270}.

Mathematica

a = {{1}, {6, 10}, {16, 22, 30, 42}, {16, 16, 22, 30, 30, 42}, {27, 34, 49, 52, 66, 75, 96}, {58, 92, 114, 136, 168, 182, 220, 270}}; Flatten[a]

Crossrefs

Cf. A120668 (rows sums), A124680, A129766.

Sequence in context: A315346 A315347 A315348 * A301724 A315349 A315350

Adjacent sequences: A129841 A129842 A129843 * A129845 A129846 A129847

Keyword

nonn,fini,full,tabf

Author

Roger L. Bagula, May 22 2007

Extensions

Edited by N. J. A. Sloane, Dec 30 2008

a(26) corrected by Andrey Zabolotskiy, Jul 23 2024

Status

approved