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

Author

Reinhard Zumkeller, Jul 16 2007

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)

Formula

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

Extensions

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