|
| |
|
|
A034404
|
|
Values of C(n,3) which can be written as C(x,3)+C(y,3).
|
|
2
| |
|
|
20, 680, 29260, 34220, 70300, 221815, 227920, 287980, 467180, 908600, 2481115, 4278680, 12259940, 13813570, 15493204, 17861900, 19970444, 24672560, 25665020, 27880600, 29742164, 34055980, 44722580
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| Bombieri's Napkin Problem: Bombieri said that "the equation C(x,n)+C(y,n)=C(z,n) has no trivial solutions for n >= 3" (the joke being that he said "trivial" rather than "nontrivial"!).
Also: tetrahedral numbers that are the sum of two other tetrahedral numbers. (For the indices of these terms, see A002311.)[From Harvey P. Dale, Jul 25 2011]
|
|
|
REFERENCES
| Van der Poorten, Notes on Fermat's Last Theorem, Wiley, p. 122.
|
|
|
EXAMPLE
| C(10,3)+C(16,3)=C(17,3)=680.
|
|
|
MATHEMATICA
| With[{tetras=Binomial[Range[700]+2, 3]}, Union[Select[Total/@Tuples[ tetras, 2], MemberQ[tetras, #]&]]] (* From Harvey P. Dale, Jul 25 2011 *)
|
|
|
CROSSREFS
| Cf. A010330, A002311.
Sequence in context: A006410 A159874 A203136 * A179712 A012802 A049214
Adjacent sequences: A034401 A034402 A034403 * A034405 A034406 A034407
|
|
|
KEYWORD
| nonn,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
