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

Author

Roger L. Bagula, May 22 2007

Keywords

• nonn
• fini
• full
• tabf

Examples

			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}.
		

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.

Crossrefs

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

Programs

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]

Extensions

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

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