A121984 a(n) = number of solutions to the Diophantine equation x+y^2+z^3=n^4 with positive x,y,z all distinct.

0, 3, 23, 69, 155, 293, 508, 799, 1205, 1732, 2395, 3218, 4216, 5412, 6821, 8502, 10416, 12629, 15137, 17996, 21173, 24768, 28755, 33164, 38020, 43341, 49162, 55550, 62485, 70004, 78123, 86862, 96254, 106392, 117211, 128754, 141147, 154276

Offset

1,2

Links

Table of n, a(n) for n=1..38.

Example

a(2)=3 because there are 3 solutions to equation x+y^2+z^3=2^4 with all distinct {x,y,z}={6,3,1},{7,1,2},{11,2,1}.
a(3)=23 because there are 23 solutions to equation x+y^2+z^3=3^4 with all distinct {x, y, z}={5, 7, 3}, {8, 3, 4}, {9, 8, 2}, {13, 2, 4}, {16, 1, 4}, {16, 8, 1}, {18, 6, 3}, {24, 7, 2}, {29, 5, 3}, {31, 7, 1}, {37, 6, 2}, {38, 4, 3}, {44, 6, 1}, {48, 5, 2}, {50, 2, 3}, {53, 1, 3}, {55, 5, 1}, {57, 4, 2}, {64, 3, 2}, {64, 4, 1}, {71, 3, 1}, {72, 1, 2}, {76, 2, 1}.

Maple

A121984 := proc(n) local res, x, y, z, n4 ; res := 0 ; n4 := n^4 ; for y from 1 to n^2 do for z from 1 to n^2 do x := n4-y^2-z^3 ; if x > 0 and x <> y and x <> z and y<> z then res := res+1 ; fi ; if x < 0 then break ; fi ; od ; od ; RETURN(res) ; end ; for n from 1 to 60 do printf("%d, ", A121984(n)) ; od ; # R. J. Mathar, Jan 13 2007

Crossrefs

Cf. A121876 = Diophantine equation x+y^2+z^3=n^4.

Sequence in context: A358422 A196325 A003531 * A107177 A096207 A163210

Adjacent sequences: A121981 A121982 A121983 * A121985 A121986 A121987

Keyword

nonn

Author

Zak Seidov, Sep 09 2006

Extensions

More terms from R. J. Mathar, Jan 13 2007

Status

approved