A002609 Glaisher's function G(n) (18 squares version).

1, -20, -80, 144, 610, -448, -1120, 2240, -3423, -12200, 14800, 29440, -5470, -6272, -48800, -81664, 73090, 68460, 15600, 87840, -139776, 82880, 189920, -474112, -18525, 109400, -251040, 412160, -128222, -273280, 54400, 1059840, 1847040

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. 311). [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

Different from A002111 (another Glaisher G(n)).

Formula

a(n) = A002611(2*n) - 16*A002611(n). - 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