A176975 Dimension arising in an indefinite quaternion algebra over Q.

0, -1, 0, -1, 1, 2, 2, 2, 3, 4, 6, 6, 8, 8, 11, 13, 15, 17, 19, 22, 27, 29, 33, 36, 42, 47, 52, 57, 63, 70, 78, 84, 93, 100, 110, 120, 130, 140, 151, 163, 177, 189, 203, 216, 233, 249, 265, 282, 300, 319, 340, 359, 381, 402, 426, 450, 475, 500, 526, 554, 584

Offset

0,6

Comments

See reference for precise definition. The definition makes sense only for n > 4. All terms are generated using the formula given by Kitayama (and here in the Python code), but for n <= 4 they don't have meaningful interpretation.

Links

Table of n, a(n) for n=0..60.

Hidetaka Kitayama, On the graded ring of Siegel modular forms of degree two with respect to a non-split symplectic group, arXiv:1004.5164 [math.NT], 2010. See table at p. 4.

Hidetaka Kitayama, On the graded ring of Siegel modular forms of degree two with respect to a non-split symplectic group, International Journal of Mathematics 23 (2012), 1250032. See Sec. 2.3.

Prog

(Python)
[(4*k**3-18*k**2+696*k-1737+(-1)**k*225 + [0, -1, 1][k%3]*160 + [1, 0, 0, -1][k%4]*360 + [1, 0, 0, -1, 0][k%5]*1152) // 1440 for k in range(100)] # Andrey Zabolotskiy, Sep 13 2021

Crossrefs

Sequence in context: A089150 A056697 A132427 * A333374 A098523 A350514

Adjacent sequences: A176972 A176973 A176974 * A176976 A176977 A176978

Keyword

sign

Author

Jonathan Vos Post, Apr 29 2010

Extensions

Terms a(11) and beyond from Andrey Zabolotskiy, Sep 13 2021

Status

approved