A045634 Number of ways in which n can be partitioned as a sum of a square and cube.

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

Offset

0,2

Comments

a(A022550(n))=0; a(A179509(n))=1; a(A022549(n))>0; a(A060861(n))=n. [From Reinhard Zumkeller, Jul 17 2010]

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

Example

a(9)=2 because 9=2^3+1^2 and 9=3^2+0^3.

Maple

M:=100; M2:=M^2; t0:=array(0..M2);
for i from 0 to M2 do t0[i]:=0; od:
for a from 0 to M do for b from 0 to M do
i:=a^2+b^3; if i <= M2 then t0[i]:=t0[i]+1; fi; od: od:
[seq(t0[i], i=0..M2)];

Mathematica

max = 100; Clear[a]; a[_] = 0;
Do[n = i^2 + j^3; a[n] += 1, {i, 0, Sqrt[max]}, {j, 0, max^(1/3)}];
Table[a[n], {n, 0, max}] (* Jean-François Alcover, Aug 02 2018 *)

Crossrefs

Cf. A022549, A060861, A135910, A135911, A135912.

Sequence in context: A321916 A257265 A045706 * A141702 A364048 A353657

Adjacent sequences: A045631 A045632 A045633 * A045635 A045636 A045637

Keyword

nonn

Author

Felice Russo

Extensions

More terms from Erich Friedman

Status

approved