A010331 Numbers that are expressible as C(m,5) + C(n,5) in at least 2 ways.

252, 342513171, 3169663601

Offset

1,1

Comments

Did not find any other couple (m, n) with n <= m <= 600. - Michel Marcus, Feb 03 2014

No additional solutions with n <= m <= 25000 exist. Conjecture: no additional solutions exist. - Jon E. Schoenfield, Apr 13 2014

Links

Table of n, a(n) for n=1..3.

J. Leech, Some solutions of Diophantine equations, Proc. Camb. Phil. Soc., 53 (1957), 778-780.

Example

C(9,5) + C(9,5) = C(10,5) + C(4,5).
C(118,5) + C(117,5) = C(133,5) + C(78,5).
C(197,5) + C(160,5) = C(209,5) + C(53,5).

Prog

(PARI) findother(s, ma) = {forstep (i = ma-1, 4, -1, my(ci = binomial(i, 5)); if (2*ci < s, return([])); forstep (j = i, 4, -1, my(cj = binomial(j, 5)); if (ci+cj == s, return ([i, j])); ); ); return ([]); }
lista(ma, mb) = {for (m = ma, mb, my(cm = binomial(m, 5)); forstep (n = m, 4, -1, my(cn = binomial(n, 5)); my(s = cm+cn); vsol = findother(s, m); if (#vsol, print1(s, ", "); /*vsol = concat(vsol, [m, n]); print(vsol); */); ); ); } \\ Michel Marcus, Feb 03 2014

Crossrefs

Cf. A000389.

Sequence in context: A172831 A172879 A227766 * A362888 A390920 A172690

Adjacent sequences: A010328 A010329 A010330 * A010332 A010333 A010334

Keyword

nonn,more,bref

Author

N. J. A. Sloane

Status

approved