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

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

Offset

1,5

Links

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

Example

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.

Prog

(PARI) a(i, n, k)=local(s, j); if(k==1, if(issquare(n) && n<i^2, return(1), return(0)), s=0; for(j=ceil(sqrt(n/k)), min(i-1, floor(sqrt(n-k+1))), s+=a(j, n-j^2, k-1)); return(s)) for(n=1, 50, m=n^4; k=n; print1(a(m+1, m, k)", ") ) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 16 2007

Crossrefs

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).

Sequence in context: A056282 A000770 A327507 * A215766 A320819 A360499

Adjacent sequences: A133102 A133103 A133104 * A133106 A133107 A133108

Keyword

nonn

Author

Hugo Pfoertner, Sep 12 2007

Extensions

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

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

Status

approved