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 1-5 of 5 results.

A034584 Radon-Hurwitz numbers: log_2 of dimension of an irreducible R-module for Clifford algebra Cl_n.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 6, 7, 7, 7, 7, 8, 9, 10, 10, 11, 11, 11, 11, 12, 13, 14, 14, 15, 15, 15, 15, 16, 17, 18, 18, 19, 19, 19, 19, 20, 21, 22, 22, 23, 23, 23, 23, 24, 25, 26, 26, 27, 27, 27, 27, 28, 29, 30, 30, 31, 31, 31, 31
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • H. Blaine Lawson, Jr. and M.-L. Michelsohn, Spin Geometry, Princeton, p. 33.
  • Pertti Lounesto, Clifford Algebras and Spinors, Cambridge, 1997, p. 226.

Crossrefs

Cf. A003484, A034583-A034586.

Programs

  • PARI
    concat(0, Vec(x*(1+ x + x^3 + x^7)/((1 - x)*(1 - x^8)) + O(x^80))) \\ Michel Marcus, Oct 03 2014

Formula

a(n+8) = a(n) + 4, n >= 0, a(0) = 0, a(1) = 1, a(2)= a(3) = 2, a(4) = a(5) = a(6) = a(7) =3.
G.f.: x*(1+ x + x^3 + x^7)/((1 - x)*(1 - x^8)). - Wolfdieter Lang, Oct 03 2014

A034586 Log_2 of dimension of an irreducible Z_2 graded H-module for Clifford algebra Cl_n.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 4, 4, 5, 5, 5, 5, 6, 7, 8, 8, 9, 9, 9, 9, 10, 11, 12, 12, 13, 13, 13, 13, 14, 15, 16, 16, 17, 17, 17, 17, 18, 19, 20, 20, 21, 21, 21, 21, 22, 23, 24, 24, 25, 25, 25, 25, 26, 27, 28, 28, 29, 29, 29, 29, 30, 31, 32, 32, 33, 33, 33, 33, 34, 35
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • Blaine Lawson and Michelsohn, Spin Geometry, Princeton, p. 285.

Crossrefs

Cf. A034583, A034584, A034585.

Formula

a(n) = log_2(A034585(n)). - Sean A. Irvine, Aug 28 2020

Extensions

More terms from Sean A. Irvine, Aug 28 2020

A034585 Dimension of an irreducible Z_2 graded H-module for Clifford algebra Cl_n.

Original entry on oeis.org

2, 2, 2, 2, 4, 8, 16, 16, 32, 32, 32, 32, 64, 128, 256, 256, 512, 512, 512, 512, 1024, 2048, 4096, 4096, 8192, 8192, 8192, 8192, 16384, 32768, 65536, 65536, 131072, 131072, 131072, 131072, 262144, 524288, 1048576, 1048576, 2097152, 2097152, 2097152, 2097152
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • H. Blaine Lawson, Jr. and M.-L. Michelsohn, Spin Geometry, Princeton, p. 285.

Crossrefs

Cf. A034583-A034586.

Formula

a(n) = 16 * a(n-8), n > 8. - Sean A. Irvine, Aug 28 2020

Extensions

More terms from Sean A. Irvine, Aug 28 2020

A236680 Dimension of the space of spinors in n-dimensional real space.

Original entry on oeis.org

1, 2, 4, 4, 4, 4, 8, 8, 16, 32, 64, 64, 64, 64, 128, 128, 256, 512, 1024, 1024, 1024, 1024, 2048, 2048, 4096, 8192, 16384, 16384, 16384, 16384, 32768, 32768, 65536, 131072, 262144, 262144, 262144, 262144, 524288, 524288, 1048576, 2097152, 4194304
Offset: 1

Views

Author

Charles R Greathouse IV and William J. Keith, Jan 29 2014

Keywords

Comments

a(n) = n only for n = 1, 2, 4, 8. These correspond to the four normed division algebras: the real numbers, the complex numbers, the quaternions, and the octonions.
All terms are powers of 2: a(n) = 2^A236916(n-1).

Links

Crossrefs

Cf. A236916.
Closely related to A034583 and A034584.

Programs

  • Mathematica
    LinearRecurrence[{2,-2,0,4,-8,8},{1,2,4,4,4,4},50] (* Harvey P. Dale, May 05 2019 *)
  • PARI
    Vec(x*(1+2*x^2+4*x^5)/((1-2*x^2)*(1+2*x^2)*(1-2*x+2*x^2)) + O(x^100)) \\ Colin Barker, Jan 30 2014

Formula

a(n) = 16*a(n-8) = 2*a(n-1) - 2*a(n-2) + 4*a(n-4) - 8*a(n-5) + 8*a(n-6).
G.f.: x*(1+2*x^2+4*x^5)/((1-2*x^2)*(1+2*x^2)*(1-2*x+2*x^2)). - Colin Barker, Jan 30 2014

A236916 The first "octad" is 0, 1, 2, 2, 2, 2, 3, 3; thereafter add 4 to get the next octad.

Original entry on oeis.org

0, 1, 2, 2, 2, 2, 3, 3, 4, 5, 6, 6, 6, 6, 7, 7, 8, 9, 10, 10, 10, 10, 11, 11, 12, 13, 14, 14, 14, 14, 15, 15, 16, 17, 18, 18, 18, 18, 19, 19, 20, 21, 22, 22, 22, 22, 23, 23, 24, 25, 26, 26, 26, 26, 27, 27, 28, 29, 30, 30, 30, 30, 31, 31, 32, 33, 34, 34, 34, 34, 35, 35, 36, 37, 38, 38, 38, 38, 39, 39, 40, 41, 42, 42
Offset: 0

Views

Author

N. J. A. Sloane, Feb 01 2014

Keywords

Links

Crossrefs

Cf. A236680. A034583 is a very similar sequence.

Programs

  • Mathematica
    Flatten[NestList[4+#&,{0,1,2,2,2,2,3,3},10]] (* Harvey P. Dale, Oct 19 2015 *)

Formula

G.f.: (x+x^2+x^6+x^8)/((1-x)*(1-x^8)). - Robert Israel, Jun 09 2020
Showing 1-5 of 5 results.

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

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