cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 61-66 of 66 results.

A162183 Number of reduced words of length n in the Weyl group B_45.

Original entry on oeis.org

1, 45, 1034, 16170, 193544, 1890624, 15695085, 113852001, 736452870, 4313931566, 23162284321, 115106177245, 533700057015, 2324210876515, 9560626910011, 37327619195919, 138907067703060, 494486307393900, 1689330735102480
Offset: 0

Views

Author

John Cannon and N. J. A. Sloane, Nov 30 2009

Keywords

Comments

Computed with MAGMA using commands similar to those used to compute A161409.

References

  • J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
  • N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)

Formula

G.f. for B_m is the polynomial Prod_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.

A162186 Number of reduced words of length n in the Weyl group B_46.

Original entry on oeis.org

1, 46, 1080, 17250, 210794, 2101418, 17796503, 131648504, 868101374, 5182032940, 28344317261, 143450494506, 677150551521, 3001361428036, 12561988338047, 49889607533966, 188796675237026, 683282982630926, 2372613717733406
Offset: 0

Views

Author

John Cannon and N. J. A. Sloane, Nov 30 2009

Keywords

Comments

Computed with MAGMA using commands similar to those used to compute A161409.

References

  • J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
  • N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)

Formula

G.f. for B_m is the polynomial Prod_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.

A162191 Number of reduced words of length n in the Weyl group B_47.

Original entry on oeis.org

1, 47, 1127, 18377, 229171, 2330589, 20127092, 151775596, 1019876970, 6201909910, 34546227171, 177996721677, 855147273198, 3856508701234, 16418497039281, 66308104573247, 255104779810273, 938387762441199
Offset: 0

Views

Author

John Cannon and N. J. A. Sloane, Nov 30 2009

Keywords

Comments

Computed with MAGMA using commands similar to those used to compute A161409.

References

  • J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
  • N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)

Formula

G.f. for B_m is the polynomial Prod_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.

A162193 Number of reduced words of length n in the Weyl group B_48.

Original entry on oeis.org

1, 48, 1175, 19552, 248723, 2579312, 22706404, 174482000, 1194358970, 7396268880, 41942496051, 219939217728, 1075086490926, 4931595192160, 21350092231441, 87658196804688, 342762976614961, 1281150739056160
Offset: 0

Views

Author

John Cannon and N. J. A. Sloane, Nov 30 2009

Keywords

Comments

Computed with MAGMA using commands similar to those used to compute A161409.

References

  • J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
  • N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)

Formula

G.f. for B_m is the polynomial Prod_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.

A162204 Number of reduced words of length n in the Weyl group B_49.

Original entry on oeis.org

1, 49, 1224, 20776, 269499, 2848811, 25555215, 200037215, 1394396185, 8790665065, 50733161116, 270672378844, 1345758869770, 6277354061930, 27627446293371, 115285643098059, 458048619713020, 1739199358769180
Offset: 0

Views

Author

John Cannon and N. J. A. Sloane, Nov 30 2009

Keywords

Comments

Computed with MAGMA using commands similar to those used to compute A161409.

References

  • J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
  • N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)

Formula

G.f. for B_m is the polynomial Prod_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.

A162205 Number of reduced words of length n in the Weyl group B_50.

Original entry on oeis.org

1, 50, 1274, 22050, 291549, 3140360, 28695575, 228732790, 1623128975, 10413794040, 61146955156, 331819334000, 1677578203770, 7954932265700, 35582378559071, 150868021657130, 608916641370150, 2348116000139330
Offset: 0

Views

Author

John Cannon and N. J. A. Sloane, Nov 30 2009

Keywords

Comments

Computed with MAGMA using commands similar to those used to compute A161409.

References

  • J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.
  • N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche II.)

Crossrefs

Cf. A128084.

Formula

G.f. for B_m is the polynomial Product_{k=1..m}(1-x^(2k))/(1-x). Only finitely many terms are nonzero. This is a row of the triangle in A128084.
Previous Showing 61-66 of 66 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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