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.

Showing 1-10 of 10 results.

A225928 a(n) = 4*16^n + 8*4^n + 17.

Original entry on oeis.org

29, 113, 1169, 16913, 264209, 4202513, 67141649, 1073872913, 17180393489, 274880004113, 4398054899729, 70368777732113, 1125900041060369, 18014399046352913, 288230378299195409, 4611686027017322513, 73786976329197944849, 1180591620854850256913
Offset: 0

Views

Author

Eric M. Schmidt, May 21 2013

Keywords

Comments

Number of conjugacy classes in Ree group 2F4(2*4^n).

Links

Crossrefs

Cf. A188161, A224790, A225929 - A225938.

Programs

  • Mathematica
    LinearRecurrence[{21,-84,64},{29,113,1169},20] (* Harvey P. Dale, May 06 2016 *)
  • PARI
    a(n)=4*16^n+8*4^n+17 \\ Charles R Greathouse IV, May 22 2013
  • Sage
    [4*16^n + 8*4^n + 17 for n in [0..20]]

Formula

G.f.: 17/(1-x) + 8/(1-4x) + 4/(1-16x).
a(n) = 21*a(n-1) - 84*a(n-2) + 64*a(n-3) for n > 2. - Wesley Ivan Hurt, Oct 08 2017

A225929 Number of conjugacy classes in Chevalley group G_2(q) as q runs through the prime powers.

Original entry on oeis.org

16, 23, 32, 44, 72, 88, 107, 152, 204, 296, 332, 408, 584, 684, 791, 908, 1032, 1096, 1452, 1772, 1944, 2312, 2508, 2924, 3608, 3852, 4232, 4632, 5192, 5484, 6408, 6731, 7064, 8108, 9612, 10412, 10824, 11672, 12108, 13004, 14892, 15884, 16392, 16648, 17432
Offset: 1

Views

Author

Eric M. Schmidt, May 21 2013

Keywords

Links

Crossrefs

Cf. A188161, A224790, A225928 - A225938.

Programs

  • Sage
    def A225929(q) : return q^2 + 2*q + (9 if q%6 in [1,5] else 8)

Formula

Let q be the n-th prime power. Then a(n) = q^2 + 2q + c, where c = 9 if q == 1, 5 (mod 6) and c = 8 otherwise.

A225937 Number of conjugacy classes in adjoint Chevalley group E_7(q) as q runs through the prime powers.

Original entry on oeis.org

531, 4569, 24553, 105644, 992834, 2447517, 5477205, 21674822, 68494004, 287617189, 437805224, 946620206, 3567305234, 6369359984, 10879403385, 17889596996, 28462405562, 35505127221, 97646355404, 199751157632, 278452165094, 517886829194, 692659723976
Offset: 1

Views

Author

Eric M. Schmidt, May 21 2013

Keywords

Links

Crossrefs

Cf. A188161, A224790, A225928 - A225938.

Programs

  • Sage
    def A225937(q) : return q^7 + q^6 + 2*q^5 + (4*q^4 + 10*q^3 + 15*q^2 + 25*q + 21 if q%2==0 else 5*q^4 + 13*q^3 + 24*q^2 + 46*q + 57 if q%3==0 else 5*q^4 + 13*q^3 + 24*q^2 + 47*q + 59)

Formula

Let q be the n-th prime power. Then, a(n) is
q^7 + q^6 + 2q^5 + 4q^4 + 10q^3 + 15q^2 + 25q + 21 if q == 0 (mod 2);
q^7 + q^6 + 2q^5 + 5q^4 + 13q^3 + 24q^2 + 46q + 57 if q == 0 (mod 3);
q^7 + q^6 + 2q^5 + 5q^4 + 13q^3 + 24q^2 + 47q + 59 otherwise.

A225930 Number of conjugacy classes in twisted Chevalley group 3D4(q) as q runs through the prime powers.

Original entry on oeis.org

35, 126, 345, 786, 2806, 4685, 7386, 16110, 30946, 69909, 88746, 137566, 292566, 406906, 551886, 732546, 954310, 1082405, 1926226, 2896410, 3500206, 4985766, 5884906, 8042226, 12326286, 14076610, 17043525, 20456446, 25774710, 28792666, 39449446, 43584810, 48037086
Offset: 1

Views

Author

Eric M. Schmidt, May 21 2013

Keywords

Links

Crossrefs

Cf. A000961 (without 1), A188161, A224790, A225928-A225938.

Programs

  • Mathematica
    Map[(#^2 + 1)*(# + 1)*# + 5 + Mod[#, 2] &, Select[Range[100], PrimePowerQ]] (* Paolo Xausa, Jan 16 2025 *)
  • PARI
    apply(x->(x^4 + x^3 + x^2 + x + 5 + (x%2)), select(isprimepower, [1..100])) \\ Michel Marcus, Jan 16 2025

Formula

Let q be the n-th prime power. Then, a(n) = q^4 + q^3 + q^2 + q + c, where c = 5 if q is even and c = 6 if q is odd.

A225931 Number of conjugacy classes in Chevalley group F_4(q) as q runs through the prime powers.

Original entry on oeis.org

95, 273, 539, 1156, 3566, 5603, 8751, 18346, 34364, 75443, 95656, 146882, 308254, 426656, 576345, 762412, 990326, 1120595, 1985636, 2976016, 3591434, 5103526, 6017672, 8208724, 12553402, 14326796, 17326739, 20785106, 26163886, 29214704, 39981062, 44156775
Offset: 1

Views

Author

Eric M. Schmidt, May 21 2013

Keywords

Links

Crossrefs

Cf. A188161, A224790, A225928 - A225938.

Programs

  • Sage
    def A225931(q) : return q^4 + 2*q^3 + (6*q^2 + 10*q + 19 if q%2==0 else 7*q^2 + 15*q + 30 if q%3==0 else 7*q^2 + 15*q + 31)

Formula

Let q be the n-th prime power.
a(n) = q^4 + 2q^3 + 6q^2 + 10q + 19 if q == 0 mod 2.
a(n) = q^4 + 2q^3 + 7q^2 + 15q + 30 if q == 0 mod 3.
a(n) = q^4 + 2q^3 + 7q^2 + 15q + 31 otherwise.

A225932 Number of conjugacy classes in simply connected Chevalley group E_6(q) as q runs through the prime powers.

Original entry on oeis.org

180, 1269, 6116, 20454, 140886, 304548, 605685, 1965462, 5262486, 17969012, 25736406, 49802214, 155060070, 254728710, 402876885, 616803846, 918054582, 1109465220, 2638941366, 4871761782, 6475396806, 11018543046, 14135564454, 22598655270, 42920128086
Offset: 1

Views

Author

Eric M. Schmidt, May 21 2013

Keywords

Links

Crossrefs

Cf. A188161, A224790, A225928 - A225938.

Programs

  • Sage
    def A225932(q) : return q^6 + q^5 + 2*q^4 + 2*q^3 + [15*q^2 + 21*q + 60, 6*q^2 + 4*q + 4, 7*q^2 + 5*q + 3, 14*q^2 + 20*q + 52, 7*q^2 + 5*q + 4][q%6-1]

Formula

Let q be the n-th prime power.
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 15q^2 + 21q + 60 if q == 1 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 6q^2 + 4q + 4 if q == 2 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 7q^2 + 5q + 3 if q == 3 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 14q^2 + 20q + 52 if q == 4 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 7q^2 + 5q + 4 if q == 5 (mod 6).

A225933 Number of conjugacy classes in adjoint Chevalley group E_6(q) as q runs through the prime powers.

Original entry on oeis.org

180, 1269, 5940, 20454, 140470, 304548, 605685, 1965462, 5261278, 17967252, 25736406, 49799782, 155060070, 254724622, 402876885, 616803846, 918048406, 1109465220, 2638932670, 4871761782, 6475385158, 11018543046, 14135549422, 22598655270, 42920128086
Offset: 1

Views

Author

Eric M. Schmidt, May 21 2013

Keywords

Links

Crossrefs

Cf. A188161, A224790, A225928 - A225938.

Programs

  • Sage
    def A225933(q) : return q^6 + q^5 + 2*q^4 + 2*q^3 + [9*q^2 + 9*q + 22, 6*q^2 + 4*q + 4, 7*q^2 + 5*q + 3, 8*q^2 + 8*q + 20, 7*q^2 + 5*q + 4][q%6-1]

Formula

Let q be the n-th prime power.
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 9q^2 + 9q + 22 if q == 1 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 6q^2 + 4q + 4 if q == 2 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 7q^2 + 5q + 3 if q == 3 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 8q^2 + 8q + 20 if q == 4 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 2q^3 + 7q^2 + 5q + 4 if q == 5 (mod 6).

A225934 Number of conjugacy classes in simply connected twisted Chevalley group 2E6(q) as q runs through the prime powers.

Original entry on oeis.org

346, 1389, 6102, 21182, 141262, 306574, 607533, 1969886, 5266030, 17975982, 25750142, 49814254, 155091326, 254757166, 402919341, 616863422, 918109966, 1109543806, 2639036782, 4871920766, 6475547950, 11018778302, 14135789614, 22598987966, 42920581982
Offset: 1

Views

Author

Eric M. Schmidt, May 21 2013

Keywords

Links

Crossrefs

Cf. A188161, A224790, A225928 - A225938.

Programs

  • Sage
    def A225934(q) : return q^6 + q^5 + 2*q^4 + 4*q^3 + [11*q^2 + 11*q + 16, 18*q^2 + 26*q + 62, 11*q^2 + 11*q + 15, 10*q^2 + 10*q + 14, 19*q^2 + 27*q + 72][q%6-1]

Formula

Let q be the n-th prime power.
a(n) = q^6 + q^5 + 2q^4 + 11q^2 + 11q + 16 if q == (1 mod 6).
a(n) = q^6 + q^5 + 2q^4 + 18q^2 + 26q + 62 if q == (2 mod 6).
a(n) = q^6 + q^5 + 2q^4 + 11q^2 + 11q + 15 if q == (3 mod 6).
a(n) = q^6 + q^5 + 2q^4 + 10q^2 + 10q + 14 if q == (4 mod 6).
a(n) = q^6 + q^5 + 2q^4 + 19q^2 + 27q + 72 if q == (5 mod 6).

A225935 Number of conjugacy classes in adjoint twisted Chevalley group 2E6(q) as q runs through the prime powers.

Original entry on oeis.org

266, 1389, 6102, 20934, 141262, 306062, 607533, 1968990, 5266030, 17975982, 25748166, 49814254, 155087838, 254757166, 402919341, 616857990, 918109966, 1109537246, 2639036782, 4871910150, 6475547950, 11018764446, 14135789614, 22598970438, 42920560350
Offset: 1

Views

Author

Eric M. Schmidt, May 21 2013

Keywords

Links

Crossrefs

Cf. A188161, A224790, A225928 - A225938.

Programs

  • Sage
    def A225935(q) : return q^6 + q^5 + 2*q^4 + 4*q^3 + [11*q^2 + 11*q + 16, 12*q^2 + 14*q + 30, 11*q^2 + 11*q + 15, 10*q^2 + 10*q + 14, 13*q^2 + 15*q + 34][q%6-1]

Formula

Let q be the n-th prime power.
a(n) = q^6 + q^5 + 2q^4 + 4q^3 + 11q^2 + 11q + 16 if q == 1 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 4q^3 + 12q^2 + 14q + 30 if q == 2 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 4q^3 + 11q^2 + 11q + 15 if q == 3 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 4q^3 + 10q^2 + 10q + 14 if q == 4 (mod 6).
a(n) = q^6 + q^5 + 2q^4 + 4q^3 + 13q^2 + 15q + 34 if q == 5 (mod 6).

A225936 Number of conjugacy classes in simply connected Chevalley group E_7(q) as q runs through the prime powers.

Original entry on oeis.org

531, 5052, 24553, 107833, 999759, 2447517, 5494392, 21711067, 68562129, 287617189, 437995549, 946912755, 3567919999, 6370211253, 10880553708, 17891119105, 28464383127, 35505127221, 97650322329, 199757104357, 278459342139, 517897029319, 692671751805
Offset: 1

Views

Author

Eric M. Schmidt, May 21 2013

Keywords

Links

Crossrefs

Cf. A188161, A224790, A225928 - A225938.

Programs

  • Sage
    def A225936(q) : return q^7 + q^6 + 2*q^5 + (4*q^4 + 10*q^3 + 15*q^2 + 25*q + 21 if q%2==0 else 7*q^4 + 17*q^3 + 35*q^2 + 70*q + 99 if q%3==0 else 7*q^4 + 17*q^3 + 35*q^2 + 71*q + 103)

Formula

Let q be the n-th prime power. Then, a(n) is
q^7 + q^6 + 2q^5 + 4q^4 + 10q^3 + 15q^2 + 25q + 21 if q == 0 (mod 2);
q^7 + q^6 + 2q^5 + 7q^4 + 17q^3 + 35q^2 + 70q + 99 if q == 0 (mod 3);
q^7 + q^6 + 2q^5 + 7q^4 + 17q^3 + 35q^2 + 71q + 103 otherwise.
Showing 1-10 of 10 results.

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

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