A002609 Glaisher's function G(n) (18 squares version). (Formerly M5088 N2203)

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

1,2

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. 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

Formula

a(n) = A002611(2*n) - 16*A002611(n). - Sean A. Irvine, Mar 04 2019

Crossrefs

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

Sequence in context: A211613 A292360 A337988 * A195322 A200424 A211463

Adjacent sequences: A002606 A002607 A002608 * A002610 A002611 A002612

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