A054206 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 j values.

3, 49, 106, 306, 348, 443, 830, 1103, 5169, 6135, 6427, 7512, 10668, 12465, 14061, 18456, 20463, 17943, 21919, 27766, 38509, 41932, 53284, 54040, 67330, 78418, 102298, 135082, 238207, 286706, 279850, 319935, 373785, 665863, 734790, 759731, 995600, 987492, 998289, 1100210, 963913, 1119792, 1196684

Offset

1,1

Comments

The i values are in A054205 and k values in A054207.

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}]; (Transpose@lst)[[2]] (* Robert G. Wilson v, Jan 15 2007 *)

Crossrefs

Cf. A054205, A054207, A000292.

Sequence in context: A252171 A160763 A041523 * A063777 A359886 A212651

Adjacent sequences: A054203 A054204 A054205 * A054207 A054208 A054209

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