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Number of ways in which n^2 can be expressed as the sum of exactly five positive squares.
1

%I #15 Oct 25 2018 22:18:05

%S 0,0,0,1,1,1,2,5,2,6,6,9,9,15,8,25,20,21,25,39,26,46,44,57,49,71,52,

%T 102,81,81,99,145,92,156,126,164,160,204,151,247,217,236,245,326,211,

%U 357,319,381,360,416,344,518,446,476,450,670,468,675,607,661,668,825,625

%N Number of ways in which n^2 can be expressed as the sum of exactly five positive squares.

%C As n goes to infinity the ratio of a(n)/a(n) of sequence A178898 (using all different squares) tends to 5/4.

%H Alois P. Heinz, <a href="/A179015/b179015.txt">Table of n, a(n) for n = 1..740</a>

%F Asymptotic behavior for large values of n is a(n) = n^2/2-47n/2+243.

%F a(n) = A025429(n^2). - _R. J. Mathar_, Jun 26 2010

%F a(n) = A065459(n) - A065458(n). - _Alois P. Heinz_, Oct 25 2018

%p a(8) = 5 since 64 can be expressed in five different ways as the sum of 5 squares (order is ignored): 8^2 = 7^2+3^2+2^2+1^2+1^2 = 6^2+5^2+1^2+1^2+1^2 = 6^2+4^2+2^2+2^2+2^2 = 6^2+3^2+3^2+3^2+1^2 = 5^2+5^2+3^2+1^2+1^2.

%Y Cf. A000290, A178898.

%Y Cf. A000132. - _R. J. Mathar_, Jun 26 2010

%Y Cf. A065458, A065459.

%K nonn

%O 1,7

%A _Carmine Suriano_, Jun 24 2010