login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A322031 (Sum_{t=0..oo} ((-1)^t*(2*t+1)*q^((2*t+1)^2)))^3 * (Sum_{t=0..oo} q^((2*t+1)^2)) = Sum_{k=0..oo} a(k)*q^(8*k+4). 0
1, -8, 18, 16, -111, 72, 178, -144, -126, -232, 384, 432, -301, 240, -1422, -192, 1728, 288, 530, -1424, 162, -888, -1998, 2016, 1633, 1008, 594, 1296, -5568, -1368, 626, -1776, 3204, 632, 10368, -4464, -6686, 2408, -3456, 800, -3231, -2664 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is Glaisher's Q(m).

REFERENCES

J. W. L. Glaisher, On the representations of a number as a sum of four squares, and on some allied arithmetical functions, Quarterly Journal of Pure and Applied Mathematics, 36 (1905), 305-358. See p. 340.

Glaisher, J. W. L. (1906). The arithmetical functions P(m), Q(m), Omega{m). Quart. J. Math, 37, 36-48.

LINKS

Table of n, a(n) for n=0..41.

J. W. L. Glaisher, On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares, Quart. J. Math. 38 (1907), 1-62 (see p. 5).

Index entries for sequences mentioned by Glaisher

MAPLE

Q1:= (add( (-1)^t*(2*t+1)*q^((2*t+1)^2), t=0..1001))^3 * (add(q^((2*t+1)^2), t=0..1001))^1;

Q2:=series(Q1, q, 1000); Q3 := seriestolist(Q2);

Q4:=[seq(Q3[8*i+5], i=0..120)];

CROSSREFS

Sequence in context: A133202 A217424 A332969 * A196207 A196474 A251258

Adjacent sequences:  A322028 A322029 A322030 * A322032 A322033 A322034

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Nov 24 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 22:46 EST 2021. Contains 349445 sequences. (Running on oeis4.)