A034404 Values of C(n,3) which can be written as C(x,3) + C(y,3).

20, 680, 29260, 34220, 70300, 221815, 227920, 287980, 467180, 908600, 2481115, 4278680, 12259940, 13813570, 15493204, 17861900, 19970444, 24672560, 25665020, 27880600, 29742164, 34055980, 44722580

Offset

1,1

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.) - Harvey P. Dale, Jul 25 2011

References

Van der Poorten, Notes on Fermat's Last Theorem, Wiley, p. 122.

Links

Delbert L. Johnson, Table of n, a(n) for n = 1..672

Formula

a(n) = A000292(A002311(n)). - Reinhard Zumkeller, May 02 2014

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, #]&]]] (* Harvey P. Dale, Jul 25 2011 *)

Prog

(Haskell)
a034404 = a000292 . a002311  -- Reinhard Zumkeller, May 02 2014

Crossrefs

Cf. A000292, 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

Extensions

Offset corrected by Andrew Howroyd, Mar 23 2023

Status

approved