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A010331 Numbers that are expressible as C(m,5) + C(n,5) in at least 2 ways. 0
252, 342513171, 3169663601 (list; graph; refs; listen; history; text; internal format)
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 * A172690 A088851 A244168

Adjacent sequences:  A010328 A010329 A010330 * A010332 A010333 A010334

KEYWORD

nonn,more,bref

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 22 10:39 EDT 2021. Contains 348160 sequences. (Running on oeis4.)