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%I #27 Mar 25 2023 13:22:39
%S 20,680,29260,34220,70300,221815,227920,287980,467180,908600,2481115,
%T 4278680,12259940,13813570,15493204,17861900,19970444,24672560,
%U 25665020,27880600,29742164,34055980,44722580
%N Values of C(n,3) which can be written as C(x,3) + C(y,3).
%C 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"!).
%C 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
%D Van der Poorten, Notes on Fermat's Last Theorem, Wiley, p. 122.
%H Delbert L. Johnson, <a href="/A034404/b034404.txt">Table of n, a(n) for n = 1..672</a>
%F a(n) = A000292(A002311(n)). - _Reinhard Zumkeller_, May 02 2014
%e C(10,3) + C(16,3) = C(17,3) = 680.
%t With[{tetras=Binomial[Range[700]+2,3]},Union[Select[Total/@Tuples[ tetras,2], MemberQ[tetras,#]&]]] (* _Harvey P. Dale_, Jul 25 2011 *)
%o (Haskell)
%o a034404 = a000292 . a002311 -- _Reinhard Zumkeller_, May 02 2014
%Y Cf. A000292, A010330, A002311.
%K nonn,nice
%O 1,1
%A _N. J. A. Sloane_
%E Offset corrected by _Andrew Howroyd_, Mar 23 2023
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