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A054208 Consider all integer triples (i,j,k), j >= k>0, with i^3=binomial(j+2,3)+binomial(k+2,3), ordered by increasing i; sequence gives i values. 3
2, 11, 45, 65, 109, 280, 644, 1079, 1309, 3180, 3355, 6864, 8284, 9700, 10681, 10856, 16775, 17094, 33506, 35650, 50435 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n)^3 is the sum of two positive tetrahedrals. j values are A054209 and k values are A054210.

LINKS

Table of n, a(n) for n=0..20.

EXAMPLE

2^3=8=binomial(2+2,3)+binomial(2+2,3); 11^3=1331=binomial(19+2,3)+binomial(3,3);

MATHEMATICA

(* Range of j values is merely empirical *) jmin[k_] := Floor[Max[k, 1.86*k - 20000]]; jmax[k_] := Ceiling[1.86*k + 16000]; jmax[3005] = 10^5; ii = Reap[ Do[ Do[i = (Binomial[j+2, 3] + Binomial[k+2, 3])^(1/3); If[IntegerQ[i], Print[{i, j, k}]; Sow[i]; Break[]], {j, jmin[k], jmax[k]}], {k, 1, 40000}] ][[2, 1]]; A054208 = Union[ii] (* Jean-Fran├žois Alcover, Dec 12 2012 *)

CROSSREFS

A054209, A054210.

Sequence in context: A181270 A110679 A127109 * A257066 A209604 A120279

Adjacent sequences:  A054205 A054206 A054207 * A054209 A054210 A054211

KEYWORD

nice,nonn

AUTHOR

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 31 2000

EXTENSIONS

More terms from Sascha Kurz, Mar 22 2002

Corrected by T. D. Noe, Oct 25 2006

STATUS

approved

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Last modified June 22 15:24 EDT 2021. Contains 345386 sequences. (Running on oeis4.)