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.

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A162149 Number of reduced words of length n in the Weyl group B_35.

Original entry on oeis.org

1, 35, 629, 7735, 73184, 567952, 3763935, 21898413, 114117990, 540864298, 2359388214, 9564192010, 36311331322, 129962338310, 440928822623, 1424753834021, 4402462293690, 13054834025406, 37266085146835
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.

A162150 Number of reduced words of length n in the Weyl group B_36.

Original entry on oeis.org

1, 36, 665, 8400, 81584, 649536, 4413471, 26311884, 140429874, 681294172, 3040682386, 12604874396, 48916205718, 178878544028, 619807366651, 2044561200672, 6447023494362, 19501857519768, 56767942666603
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

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

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.

A162165 Number of reduced words of length n in the Weyl group B_37.

Original entry on oeis.org

1, 37, 702, 9102, 90686, 740222, 5153693, 31465577, 171895451, 853189623, 3893872009, 16498746405, 65414952123, 244293496151, 864100862802, 2908662063474, 9355685557836, 28857543077604, 85625485744207
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.

A162166 Number of reduced words of length n in the Weyl group B_38.

Original entry on oeis.org

1, 38, 740, 9842, 100528, 840750, 5994443, 37460020, 209355471, 1062545094, 4956417103, 21455163508, 86870115631, 331163611782, 1195264474584, 4103926538058, 13459612095894, 42317155173498, 127942640917705
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.

A162168 Number of reduced words of length n in the Weyl group B_39.

Original entry on oeis.org

1, 39, 779, 10621, 111149, 951899, 6946342, 44406362, 253761833, 1316306927, 6272724030, 27727887538, 114598003169, 445761614951, 1641026089535, 5744952627593, 19204564723487, 61521719896985, 189464360814690
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.

A162176 Number of reduced words of length n in the Weyl group B_40.

Original entry on oeis.org

1, 40, 819, 11440, 122589, 1074488, 8020830, 52427192, 306189025, 1622495952, 7895219982, 35623107520, 150221110689, 595982725640, 2237008815175, 7981961442768, 27186526166255, 88708246063240, 278172606877930
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.

A162178 Number of reduced words of length n in the Weyl group B_41.

Original entry on oeis.org

1, 41, 860, 12300, 134889, 1209377, 9230207, 61657399, 367846424, 1990342376, 9885562358, 45508669878, 195729780567, 791712506207, 3028721321382, 11010682764150, 38197208930405, 126905454993645, 405078061871575
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.

A162179 Number of reduced words of length n in the Weyl group B_42.

Original entry on oeis.org

1, 42, 902, 13202, 148091, 1357468, 10587675, 72245074, 440091498, 2430433874, 12315996232, 57824666110, 253554446677, 1045266952884, 4073988274266, 15084671038416, 53281879968821, 180187334962466, 585265396834041
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.

A162181 Number of reduced words of length n in the Weyl group B_43.

Original entry on oeis.org

1, 43, 945, 14147, 162238, 1519706, 12107381, 84352455, 524443953, 2954877827, 15270874059, 73095540169, 326649986846, 1371916939730, 5445905213996, 20530576252412, 73812456221233, 253999791183699, 839265188017740
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.

A162182 Number of reduced words of length n in the Weyl group B_44.

Original entry on oeis.org

1, 44, 989, 15136, 177374, 1697080, 13804461, 98156916, 622600869, 3577478696, 18848352755, 91943892924, 418593879770, 1790510819500, 7236416033496, 27766992285908, 101579448507141, 355579239690840, 1194844427708580
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.
Previous Showing 51-60 of 66 results. Next

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

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