login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A121876 a(n) = number of solutions to the Diophantine equation x+y^2+z^3=n^4 with positive x,y,z. 2
0, 5, 27, 75, 163, 303, 521, 815, 1223, 1753, 2419, 3245, 4246, 5445, 6857, 8541, 10459, 12675, 15187, 18049, 21230, 24829, 28820, 33232, 38092, 43417, 49243, 55634, 62573, 70096, 78220, 86963, 96359, 106501, 117325, 128873, 141269 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..214

EXAMPLE

a(2)=5 because there are five solutions to equation x+y^2+z^3=2^4 with {x,y,z}={4,2,2},{6,3,1},{7,1,2},{11,2,1},{14,1,1};

a(3)=27 because there are 27 solutions to equation x+y^2+z^3=3^4 with

{x, y, z}={1, 4, 4}, {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}, {45, 3, 3}, {48, 5, 2}, {50, 2, 3}, {53, 1, 3}, {55, 5, 1}, {57, 4, 2}, {64, 3, 2}, {64, 4, 1}, {69, 2, 2}, {71, 3, 1}, {72, 1, 2}, {76, 2, 1}, {79, 1, 1}

PROG

(C++) #include <iostream> #include <math.h> #include <limits.h> using namespace std ; int main(int argc, char *argv[]) { const int nmax=sqrt(sqrt(INT_MAX)) ; for(int n=1; n < nmax ; n++) { int a=0 ; const int n4=n*n*n*n ; for(int z=1; ; z++) { const int z3=z*z*z ; if( z3 >= n4) break ; for(int y=1; y*y+z3 < n4 ; y++) { if ( n4-z3-y*y > 0) a++ ; } } cout << n << " " << a << endl ; } return 0 ; } - R. J. Mathar, Sep 12 2006

CROSSREFS

Sequence in context: A136917 A181890 A048712 * A137116 A137117 A064675

Adjacent sequences:  A121873 A121874 A121875 * A121877 A121878 A121879

KEYWORD

nonn

AUTHOR

Zak Seidov, Sep 09 2006

EXTENSIONS

More terms from R. J. Mathar and Max Alekseyev, Sep 10 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)