A002611 Glaisher's function V(n).

0, 1, 4, -4, -32, -16, 56, 80, 192, 98, -740, -704, 96, -224, 2440, 3520, -2624, -351, -780, -10632, 2688, 2960, -9496, 18176, 14208, -3934, 12552, -9856, -24608, -9760, -2720, -25344, -35520, 31106, 34160, 62844, 84576, 3120, -21880, -82272, 27520, -96768, -237316, 130240, -92832, 37984, 305296, -183296, 37632, 208803

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. 320). [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

• Index entries for sequences mentioned by Glaisher

Crossrefs

Cf. A002288, A004018.

Formula

a(n) = Sum_{k=1..floor(n/2)} A004018(n - 2*k) * A002288(k). - 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