A010330 -id:A010330 - cp's OEIS frontend

A002311 Numbers k such that the k-th tetrahedral number is the sum of 2 tetrahedral numbers.

4, 15, 55, 58, 74, 109, 110, 119, 140, 175, 245, 294, 418, 435, 452, 474, 492, 528, 535, 550, 562, 588, 644, 688, 702, 714, 740, 747, 753, 818, 868, 908, 918, 1098, 1158, 1220, 1241, 1428, 1434, 1444, 1450, 1645, 1708, 1738, 1786, 1868, 2170, 2183, 2220, 2256

Offset: 1

N. J. A. Sloane

Indices of A034404. - Harvey P. Dale, Jul 25 2011

Aviezri S. Fraenkel, Diophantine equations involving generalized triangular and tetrahedral numbers, pp. 99-114 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 1..463
H. Finner and K. Strassburger, Increasing sample sizes do not necessarily increase the power of UMPU-tests for 2 X 2-tables, Metrika, 54, 77-91, (2001).
M. Wunderlich, Certain properties of pyramidal and figurate numbers, Math. Comp., 16 (1962), 482-486.

Cf. A000292, A010330, A034404.

import Data.List (intersect)
a002311 n = a002311_list !! (n-1)
a002311_list = filter f [1..] where
   f x = not $ null $ intersect txs $ map (tx -) $ txs where
       txs = takeWhile (< tx) a000292_list; tx = a000292 x
-- Reinhard Zumkeller, May 02 2014

With[{tetras=Binomial[Range[1100]+2,3]},Flatten[Position[tetras,#]&/@ Union[Select[Total/@Tuples[tetras,2],MemberQ[tetras,#]&]]]] (* Harvey P. Dale, Jul 26 2011 *)

a(n) = A010330(n) - 2. - Reinhard Zumkeller, May 02 2014

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

Original entry on oeis.org

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

N. J. A. Sloane

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

			C(10,3) + C(16,3) = C(17,3) = 680.

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

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

Cf. A000292, A010330, A002311.

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

With[{tetras=Binomial[Range[700]+2,3]},Union[Select[Total/@Tuples[ tetras,2], MemberQ[tetras,#]&]]] (* Harvey P. Dale, Jul 25 2011 *)

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

Offset corrected by Andrew Howroyd, Mar 23 2023

cp's OEIS Frontend

A002311 Numbers k such that the k-th tetrahedral number is the sum of 2 tetrahedral numbers.

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