A025452 Number of partitions of n into 8 nonnegative cubes.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 3, 2, 3, 2, 2, 2, 1, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 2, 3, 2, 1, 2, 1, 2, 2, 2, 2

Offset

0,9

Comments

a(n) = 0 only for n = 23 and 239, as these two are the only numbers requiring at least nine cubes in any partition into cubes (cf. Dickson, 1939). - Felix Fröhlich, Sep 09 2017

Links

Felix Fröhlich, Table of n, a(n) for n = 0..10000

L. E. Dickson, All integers except 23 and 239 are sums of eight cubes, Bulletin of the American Mathematical Society, Vol. 45, No. 8 (1939), 588-591.

Prog

(PARI) cubes(bound) = my(v=[], x=0); while(1, v=concat(v, [x^3]); x++; if(x^3 > bound, return(v)))
a(n) = my(i=0, c=cubes(n)); for(s=1, #c, for(t=s, #c, for(u=t, #c, for(v=u, #c, for(w=v, #c, for(x=w, #c, for(y=x, #c, for(z=y, #c, if(n==c[s]+c[t]+c[u]+c[v]+c[w]+c[x]+c[y]+c[z], i++))))))))); i \\ Felix Fröhlich, Sep 09 2017

Crossrefs

Sequence in context: A322817 A194325 A300547 * A299202 A194337 A365335

Adjacent sequences: A025449 A025450 A025451 * A025453 A025454 A025455

Keyword

nonn

Author

David W. Wilson

Status

approved