A131799 Number of partitions of n into parts that are squares or cubes.

1, 1, 1, 1, 2, 2, 2, 2, 4, 5, 5, 5, 7, 8, 8, 8, 12, 14, 15, 15, 19, 21, 22, 22, 28, 33, 35, 37, 43, 48, 50, 52, 61, 69, 74, 78, 90, 98, 103, 107, 122, 135, 143, 152, 170, 186, 194, 203, 225, 247, 261, 275, 305, 330, 348, 362, 396, 429, 454, 477, 519, 561, 590, 618, 666, 717

Offset

0,5

Comments

a(n) = A078635(n) for n < 32 = 2^5.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

G.f.: Product_{k>=1} (1 - x^(k^6)) / ((1 - x^(k^2)) * (1 - x^(k^3))). - Vaclav Kotesovec, Jan 12 2017

Example

a(10) = #{9+1, 8+1+1, 4+4+1+1, 4+1+1+1+1+1+1, 1+1+1+1+1+1+1+1+1+1} = 5.

Mathematica

nmax = 65; c2max = nmax^(1/2); c3max = nmax^(1/3);
s = Flatten[{Table[n^2, {n, 1, c2max}]}~Join~{Table[n^3, {n, 1, c3max}]}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* Robert Price, Jul 31 2020 *)

Crossrefs

Cf. A000041, A001156, A002760, A003108, A078635.

Sequence in context: A125584 A230447 A029078 * A078635 A286305 A046768

Adjacent sequences: A131796 A131797 A131798 * A131800 A131801 A131802

Keyword

nonn

Author

Reinhard Zumkeller, Jul 16 2007

Extensions

a(0)=1 prepended by Ilya Gutkovskiy, Jan 11 2017

Status

approved