A133104 -id:A133104 - cp's OEIS frontend

A133103 Number of partitions of n^3 into n nonzero squares.

1, 1, 2, 1, 10, 34, 156, 734, 3599, 18956, 99893, 548373, 3078558, 17510598, 101960454, 599522778, 3565904170, 21438347021, 129905092421, 794292345434, 4890875249113, 30326545789640, 189195772457341, 1187032920371427

Offset: 1

Hugo Pfoertner, Sep 11 2007

nonn

			a(2)=1 because the only way to express 2^3 = 8 as a sum of two squares is 8 = 2^2 + 2^2.
a(3)=2 because 3^3 = 27 = 1^2 + 1^2 + 5^2 = 3^2 + 3^2 + 3^2.

Robert Gerbicz, May 09 2008, Table of n, a(n) for n = 1..40

Cf. A000161, A000378, A000141, A005875, A000118, A000132, A008451.

Cf. A133102 (number of ways to express n^3 as a sum of n distinct nonzero squares), A133104 (number of ways to express n^4 as a sum of n nonzero squares).

a(i, n, k)=local(s, j); if(k==1, if(issquare(n), return(1), return(0)), s=0; for(j=ceil(sqrt(n/k)), min(i, floor(sqrt(n-k+1))), s+=a(j, n-j^2, k-1)); return(s)) for(n=1,50, m=n^3; k=n; print1(a(m, m, k)", ") ) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007

2 more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007

More terms from Robert Gerbicz, May 09 2008

A133105 Number of partitions of n^4 into n distinct nonzero squares.

Original entry on oeis.org

1, 0, 1, 0, 21, 266, 2843, 55932, 884756, 13816633, 283194588, 5375499165, 125889124371, 3202887665805, 80542392920980, 2270543992935431, 64253268814048352, 1892633465941308859, 59116753827795287519, 1886846993941912938452

Offset: 1

Hugo Pfoertner, Sep 12 2007

nonn

			a(3)=1 because there is exactly one way to express 3^4 as the sum of 3 distinct nonzero squares: 81 = 1^2 + 4^2 + 8^2.

Robert Gerbicz, May 09 2008, Table of n, a(n) for n = 1..20

Cf. A000161, A000378, A000141, A005875, A000118, A000132, A008451.

Cf. A133104 (number of ways to express n^4 as a sum of n nonzero squares), A133102 (number of ways to express n^3 as a sum of n distinct nonzero squares).

a(i, n, k)=local(s, j); if(k==1, if(issquare(n) && n

a(10) from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007

a(11) onwards from Robert Gerbicz, May 09 2008

cp's OEIS Frontend

A133103 Number of partitions of n^3 into n nonzero squares.

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