|
Search: id:A054223
|
|
|
| A054223 |
|
Consider all integer triples (i,j,k), j,k>0, with binomial(i+2,3)=binomial(j+2,3)+k^3, ordered by increasing i; sequence gives k values. |
|
+0
3
|
|
| 4, 4, 6, 11, 9, 26, 16, 25, 110, 36, 49, 64, 335, 81, 276, 100, 649, 121, 144, 169, 196, 225, 670, 2024, 256, 1166, 289, 517, 324, 3522, 361, 3068, 4071, 400, 2485, 441, 484, 6137, 529, 1534, 6816, 576, 625, 676, 729, 784, 841, 900, 961, 15851, 16199, 12099
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
i values are A054221 and j values are A054222.
|
|
EXAMPLE
|
binomial(7+2,3)=84=binomial(4+2,3)+4^3; binomial(8+2,3)=120=binomial(6+2,3)+4^3;
|
|
PROGRAM
|
(C) #include <stdio.h> #include <limits.h> #include <math.h> unsigned A000578inv(unsigned long long n) { unsigned long long n3 = (unsigned long long)cbrt((double)n) ; for(unsigned long long k= n3-1 ; k <= n3+1 ; k++) if ( k*k*k == n) return k ; return 0 ; } int main(int argc, char *argv[]) { const unsigned long long imax = cbrt((double)ULLONG_MAX)-2. ; for(unsigned i=1; i<imax; i++) { unsigned long long i3 = i*(unsigned long long)(i+1)*(unsigned long long)(i+2) ; for(unsigned j=1 ; j < i ; j++) { unsigned long long k3 = i3- j*(unsigned long long)(j+1)*(unsigned long long)(j+2) ; if( k3 % 6 == 0) { unsigned k=A000578inv(k3/6) ; if ( k ) { printf("%d, ", k) ; fflush(stdout) ; } } } } } - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 10 2006
|
|
CROSSREFS
|
A054221, A054222.
Sequence in context: A098052 A098530 A163976 this_sequence A160643 A078321 A128089
Adjacent sequences: A054220 A054221 A054222 this_sequence A054224 A054225 A054226
|
|
KEYWORD
|
nice,nonn
|
|
AUTHOR
|
Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 04 2000
|
|
EXTENSIONS
|
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 10 2006
|
|
|
Search completed in 0.002 seconds
|
