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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

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Last modified October 30 11:14 EDT 2014. Contains 248797 sequences.