A054207 Consider all integer triples (i,j,k), j >= k > 0, with binomial(i+2,3)=j^3+k^3, ordered by increasing i; sequence gives k values.

2, 31, 80, 120, 282, 17, 525, 437, 386, 2479, 5253, 3268, 2952, 3875, 8894, 7182, 9457, 16397, 3401, 8629, 1830, 2518, 19976, 37326, 55340, 21182, 98642, 56358, 150673, 17220, 211196, 185129, 223680, 98763, 219284, 138712, 145330, 532762, 676971, 68490, 776927, 405452, 26488

Offset

1,1

Comments

The i values are in A054205 and j values in A054206.

Links

Bert Dobbelaere, Table of n, a(n) for n = 1..53

Example

binomial(5+2,3)=35=2^3+3^3; binomial(95+2,3)=147440=49^3+31^3;

Mathematica

lst = {}; Do[ b = Binomial[i + 2, 3]; j = Floor[b^(1/3)]; lmt = Ceiling[j/2]; While[ k = (b - j^3)^(1/3); j > lmt && !IntegerQ[k], j-- ]; If[j != lmt, Print[{i, j, k}]; AppendTo[lst, {i, j, k}]], {i, 2, 30000}]; Last /@ lst (* Robert G. Wilson v, Jan 15 2007 *)

Crossrefs

Cf. A054205, A054206, A000292.

Sequence in context: A031920 A302361 A175446 * A104095 A282725 A030459

Adjacent sequences: A054204 A054205 A054206 * A054208 A054209 A054210

Keyword

nice,nonn

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 28 2000

Extensions

More terms from Martin Fuller, Nov 27 2006

Offset corrected by N. J. A. Sloane, Jan 14 2009

a(30)-a(36) from Jon E. Schoenfield, Jan 14 2009

a(37)-a(43) from Jon E. Schoenfield, Aug 30 2013

Status

approved