A002610 Glaisher's function H'(4n+1) (18 squares version).

0, 1, -6, -3, 82, -84, -444, 769, 1110, -2643, -860, 2901, -1176, 6277, 1170, -21315, -2308, 14244, 29442, 15540, -58194, -13338, -31886, 4080, 176682, -70715, -51240, 81489, -135728, 13137, -205350, 58826, 355974, 16380, 530932, -457944, -938748, 140329, 99462, 317157

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Comments

It would be nice to have a q-series that generates this sequence. Glaisher gives many formulas but they are difficult to follow.

References

• J. W. L. Glaisher, On the representation of a number as sum of 18 squares, Quart. J. Math. 38 (1907), 289-351 (see p. 312). [The whole 1907 volume of The Quarterly Journal of Pure and Applied Mathematics, volume 38, is freely available from Google Books]
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Sean A. Irvine, Java program (github)
• Index entries for sequences mentioned by Glaisher

Crossrefs

Cf. A002288.

Formula

See eqn. top of page 312 in Glaisher, where Theta(n) is A002288(n). - Sean A. Irvine, Mar 03 2019

Extensions

Edited and signs added by N. J. A. Sloane, Nov 26 2018

More terms from Sean A. Irvine, Mar 03 2019