A002614 Glaisher's function theta(n) (18 squares version). (Formerly M4459 N1890)

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

1,2

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

Formula

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

Crossrefs

Cf. A002288, A321546.

Sequence in context: A277634 A309130 A263686 * A333561 A187237 A095885

Adjacent sequences: A002611 A002612 A002613 * A002615 A002616 A002617

Keyword

sign

Author

N. J. A. Sloane

Extensions

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

More terms from Sean A. Irvine, Mar 04 2019

Status

approved