A002311 Numbers k such that the k-th tetrahedral number is the sum of 2 tetrahedral numbers. (Formerly M3498 N1419)

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

1,1

Comments

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

References

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).

Links

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.

Formula

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

Mathematica

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

Prog

(Haskell)
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

Crossrefs

Cf. A000292, A010330, A034404.

Sequence in context: A094821 A071723 A001559 * A102349 A219603 A268164

Adjacent sequences: A002308 A002309 A002310 * A002312 A002313 A002314

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved