A135910 -id:A135910 - cp's OEIS frontend

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

Felice Russo

nonn

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

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

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

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

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)];

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 *)

More terms from Erich Friedman

A135911 Number of 4-tuples (x,y,z,t) of nonnegative integers such that x^2+y^3+z^4+t^5 = n.

Original entry on oeis.org

1, 4, 6, 4, 2, 3, 3, 1, 1, 4, 6, 4, 2, 2, 1, 0, 2, 7, 8, 3, 1, 2, 1, 0, 2, 6, 7, 5, 5, 4, 1, 1, 4, 8, 7, 2, 3, 7, 5, 1, 2, 5, 5, 4, 6, 5, 1, 1, 3, 7, 7, 3, 5, 6, 2, 0, 2, 5, 5, 4, 5, 2, 0, 2, 6, 11, 9, 3, 4, 6, 2, 0, 2, 5, 5, 3, 4, 3, 1, 2, 4, 10, 11, 7, 6, 4, 2, 1, 1, 6, 9, 7, 5, 3, 1, 1, 4, 8, 8, 3, 4

Offset: 0

N. J. A. Sloane, Mar 07 2008

nonn

T. D. Noe, Table of n, a(n) for n = 0..10000
K. B. Ford, The representation of numbers as sums of unlike powers II, J. Amer. Math. Soc., 9 (1996), 919-940.

Cf. A045634, A135910, A135912.

Cf. A111151 (n such that a(n)=0).

A135912 Number of 5-tuples (x,y,z,t,u) of nonnegative integers such that x^2+y^3+z^4+t^5+u^6 = n.

Original entry on oeis.org

1, 5, 10, 10, 6, 5, 6, 4, 2, 5, 10, 10, 6, 4, 3, 1, 2, 9, 15, 11, 4, 3, 3, 1, 2, 8, 13, 12, 10, 9, 5, 2, 5, 12, 15, 9, 5, 10, 12, 6, 3, 7, 10, 9, 10, 11, 6, 2, 4, 10, 14, 10, 8, 11, 8, 2, 2, 7, 10, 9, 9, 7, 2, 2, 9, 21, 26, 16, 9, 13, 11, 3, 3, 11, 16, 12, 9, 9, 5, 3, 8, 21, 29, 21, 14, 12, 7, 3, 4

Offset: 0

N. J. A. Sloane, Mar 07 2008

nonn

a(n) > 0 for n <= 10000. Is there any n for which a(n) = 0?
Note that there are many famous hard problems connected with sequences A045634, A135910, A135911 and the present entry (see the Ford reference).
The graph of this sequence suggests that a(n) is never zero. Checked to 10^5. - T. D. Noe, Mar 07 2008

T. D. Noe, Table of n, a(n) for n = 0..10000
K. B. Ford, The representation of numbers as sums of unlike powers II, J. Amer. Math. Soc., 9 (1996), 919-940.

Cf. A045634, A135910, A135911.

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 na:=a^2; for b from 0 to M do nb:=na+b^3;
if nb <= M2 then for c from 0 to M do nc:=nb+c^4; if nc <= M2 then for d from 0 to M2 do nd:=nc+d^5; if nd <= M2 then for e from 0 to M2 do i:=nd+e^6; if i <= M2 then t0[i]:=t0[i]+1; fi; od: fi; od; fi; od: fi; od: od:
[seq(t0[i],i=0..M2)];
for i from 0 to M2 do if t0[i]=0 then lprint(i); fi; od:

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions

A135911 Number of 4-tuples (x,y,z,t) of nonnegative integers such that x^2+y^3+z^4+t^5 = n.

Views

Author

Keywords

Links

Crossrefs

A135912 Number of 5-tuples (x,y,z,t,u) of nonnegative integers such that x^2+y^3+z^4+t^5+u^6 = n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple