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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A104276 Number of partitions of n in which both even and odd squares occur with multiplicity 1. There is no restriction on the parts which are twice even squares. 0
1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 1, 0, 2, 3, 1, 0, 2, 3, 1, 0, 2, 5, 3, 0, 2, 5, 3, 0, 3, 6, 4, 1, 4, 7, 4, 1, 4, 9, 6, 1, 4, 10, 7, 1, 5, 12, 9, 2, 6, 13, 9, 2, 6, 15, 12, 3, 6, 17, 14, 3, 8, 20, 16, 4, 9, 21, 17, 5, 10, 25, 22, 7, 10, 27, 24, 7, 12, 32, 28, 9, 14, 34, 30, 10, 15, 39, 37 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

LINKS

Table of n, a(n) for n=0..90.

FORMULA

G.f.: product_{k>0}((1+x^(2k-1)^2)/(1-x^(2k)^2)= Product_{k>0}((1+x^(2k-1)^2)*(1+x^(2k)^2)))/(1-x^2(2k)^2).

EXAMPLE

E.g. a(30)=3 because we can write 30 as 25+4+1=16+9+4+1=8+8+9+4+1

MAPLE

series(product((1+x^((2*k-1)^2)))/(1-x^((2*k)^2)), k=1..100), x=0, 100);

CROSSREFS

Sequence in context: A029370 A106262 A025870 * A216191 A268834 A285914

Adjacent sequences:  A104273 A104274 A104275 * A104277 A104278 A104279

KEYWORD

nonn

AUTHOR

Noureddine Chair, Mar 01 2005

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 August 5 22:41 EDT 2021. Contains 346488 sequences. (Running on oeis4.)