A002614 Glaisher's function theta(n) (18 squares version).

0, -7, 128, -975, 4608, -16340, 48384, -124303, 281600, -583746, 1146240, -2125108, 3691008, -6151880, 10055424, -15914895, 24136704, -35748899, 52583040, -75877938, 105994240, -145580124, 200279808, -272040500, 359036928, -468767690, 615599360

Offset: 1

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. 349). [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, Table of n, a(n) for n = 1..500
• Index entries for sequences mentioned by Glaisher

Crossrefs

Cf. A002288, A321546.

Formula

a(n) = (A321546(n) - A002288(n)) / 17. - Sean A. Irvine, Mar 04 2019

Extensions

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

More terms from Sean A. Irvine, Mar 04 2019