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 21-30 of 66 results. Next

A161900 Number of reduced words of length n in the Weyl group B_22.

Original entry on oeis.org

1, 22, 252, 2002, 12396, 63734, 283107, 1116236, 3983485, 13057330, 39764011, 113533312, 306173263, 784654154, 1920802566, 4510960122, 10201294213, 22286443124, 47167714715, 96947735390, 193938666735, 378324531180, 720920510115, 1344018408150, 2454841642634
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.)

Links

Crossrefs

Row n=22 of A128084.

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.

A161930 Number of reduced words of length n in the Weyl group B_23.

Original entry on oeis.org

1, 23, 275, 2277, 14673, 78407, 361514, 1477750, 5461235, 18518565, 58282576, 171815888, 477989151, 1262643305, 3183445871, 7694405993, 17895700206, 40182143330, 87349858045, 184297593435, 378236260170, 756560791350, 1477481301465, 2821499709615, 5276341352249
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.)

Links

Crossrefs

Row n=23 of A128084.

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.

A161931 Number of reduced words of length n in the Weyl group B_24.

Original entry on oeis.org

1, 24, 299, 2576, 17249, 95656, 457170, 1934920, 7396155, 25914720, 84197296, 256013184, 734002335, 1996645640, 5180091511, 12874497504, 30770197710, 70952341040, 158302199085, 342599792520, 720836052690, 1477396844040, 2954878145505, 5776377855120, 11052719207369
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.)

Links

Crossrefs

Row n=24 of A128084.

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.

A161932 Number of reduced words of length n in the Weyl group B_25.

Original entry on oeis.org

1, 25, 324, 2900, 20149, 115805, 572975, 2507895, 9904050, 35818770, 120016066, 376029250, 1110031585, 3106677225, 8286768736, 21161266240, 51931463950, 122883804990, 281186004075, 623785796595, 1344621849285, 2822018693325, 5776896838830, 11553274693950, 22605993901319
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.)

Links

Crossrefs

Row n=25 of A128084.

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.

A161933 Number of reduced words of length n in the Weyl group B_26.

Original entry on oeis.org

1, 26, 350, 3250, 23399, 139204, 712179, 3220074, 13124124, 48942894, 168958960, 544988210, 1655019795, 4761697020, 13048465756, 34209731996, 86141195946, 209025000936, 490211005011, 1113996801606, 2458618650891, 5280637344216, 11057534183046, 22610808876996
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.)

Links

Crossrefs

Row n=26 of A128084.

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.

A161859 Number of reduced words of length n in the Weyl group B_13.

Original entry on oeis.org

1, 13, 90, 442, 1728, 5720, 16653, 43745, 105586, 237354, 502113, 1007773, 1931631, 3554747, 6308719, 10837683, 18078554, 29362618, 46541560, 72140848, 109543070, 163203326, 238898101, 344008185, 487835165, 681949801, 940569228, 1280958420, 1723849738, 2293872698, 3019984381
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.)

Links

Crossrefs

Row n=13 of A128084.

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.

A161862 Number of reduced words of length n in the Weyl group B_14.

Original entry on oeis.org

1, 14, 104, 546, 2274, 7994, 24647, 68392, 173978, 411332, 913445, 1921218, 3852849, 7407596, 13716315, 24553998, 42632552, 71995170, 118536730, 190677578, 300220648, 463423974, 702322075, 1046330260, 1534165425, 2216115226, 3156684454, 4437642874, 6161492611, 8455365296
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.)

Links

Crossrefs

Row n=14 of A128084.

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.

A161875 Number of reduced words of length n in the Weyl group B_15.

Original entry on oeis.org

1, 15, 119, 665, 2939, 10933, 35580, 103972, 277950, 689282, 1602727, 3523945, 7376794, 14784390, 28500705, 53054703, 95687255, 167682425, 286219155, 476896733, 777117381, 1240541355, 1942863430, 2989193690, 4523359115, 6739474341, 9896158795, 14333801669, 20495294280
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.)

Links

Crossrefs

Row n=15 of A128084.

Programs

  • Maple
    G:= normal(mul((1-x^(2*k))/(1-x), k=1..15)):
seq(coeff(G, x, j), j=0..15^2); # Robert Israel, Nov 26 2017

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.

Extensions

a(28) corrected by Sean A. Irvine, Mar 23 2025

A161876 Number of reduced words of length n in the Weyl group B_16.

Original entry on oeis.org

1, 16, 135, 800, 3739, 14672, 50252, 154224, 432174, 1121456, 2724183, 6248128, 13624922, 28409312, 56910017, 109964720, 205651975, 373334400, 659553555, 1136450288, 1913567669, 3154109024, 5096972454, 8086166144, 12609525259, 19348999600, 29245158395, 43578960064
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.)

Links

Crossrefs

Row n=16 of A128084.

Programs

  • Maple
    G:= normal(mul((1-x^(2*k))/(1-x),k=1..16)):
seq(coeff(G,x,j),j=0..256); # Robert Israel, Mar 31 2017

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.

A161877 Number of reduced words of length n in the Weyl group B_17.

Original entry on oeis.org

1, 17, 152, 952, 4691, 19363, 69615, 223839, 656013, 1777469, 4501652, 10749780, 24374702, 52784014, 109694031, 219658751, 425310726, 798645126, 1458198681, 2594648969, 4508216638, 7662325662, 12759298116, 20845464260, 33454989519
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.)

Links

Crossrefs

Row n=17 of A128084.

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 21-30 of 66 results. Next

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

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