login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A093115 Number of partitions of n^2 into squares not greater than n. 4
1, 1, 1, 1, 5, 7, 10, 13, 17, 108, 159, 228, 317, 430, 572, 748, 5753, 8125, 11266, 15376, 20672, 27430, 35942, 46575, 59717, 523905, 708028, 946875, 1253880, 1645224, 2140099, 2761318, 3535658, 4494602, 5674753, 7118724, 69766770, 90940578, 117756370 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..500

FORMULA

Coefficient of x^(n^2) in the series expansion of Product_{k=1..floor(sqrt(n))} 1/(1 - x^(k^2)). - Vladeta Jovovic, Mar 24 2004

EXAMPLE

n=6: 6^2 = 9*2^2 = 8*2^2+4*1^2 = 7*2^2+8*1^2 = 6*2^2+12*1^2 = 5*2^2+16*1^2 = 4*2^2+20*1^2 = 3*2^2+24*1^2 = 2*2^2+28*1^2 = 1*2^2+32*1^2 = 36*1^2, therefore a(6)=10.

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1,

     `if`(i<1, 0, b(n, i-1) +`if`(i^2>n, 0, b(n-i^2, i))))

    end:

a:= proc(n) local r; r:= isqrt(n);

      b(n^2, r-`if`(r^2>n, 1, 0))

    end:

seq(a(n), n=0..50);  # Alois P. Heinz, Apr 15 2013

CROSSREFS

Cf. A093116, A092362, A001156, A037444, A078134.

Cf. A072925.

Cf. A072213, A161407. [Reinhard Zumkeller, Jun 10 2009]

Sequence in context: A196175 A112251 A089061 * A020936 A025074 A065503

Adjacent sequences:  A093112 A093113 A093114 * A093116 A093117 A093118

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Mar 21 2004

EXTENSIONS

More terms from Vladeta Jovovic, Mar 24 2004

Corrected a(0) by Alois P. Heinz, Apr 15 2013

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified November 22 20:13 EST 2014. Contains 249827 sequences.