A133105 - OEIS

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

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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