A111638 Numbers having a unique partition into three positive triangular numbers.

3, 5, 7, 8, 9, 10, 13, 14, 15, 16, 18, 24, 25, 36, 38, 50, 53, 55, 60, 69, 81, 83, 99, 110, 119

Offset

1,1

Comments

A063993(a(n)) = 1. - Reinhard Zumkeller, Jul 20 2012

Links

Table of n, a(n) for n=1..25.

Example

Example: 119=55+36+28

Mathematica

trig[n_]:=n(n+1)/2; trigInv[x_]:=Ceiling[Sqrt[Max[0, 2x]]]; lim=100; nLst=Table[0, {trig[lim]}]; Do[n=trig[a]+trig[b]+trig[c]; If[n>0 && n<=trig[lim], nLst[[n]]++ ], {a, 1, lim}, {b, a, trigInv[trig[lim]-trig[a]]}, {c, b, trigInv[trig[lim]-trig[a]-trig[b]]}]; Flatten[Position[nLst, 1]]

Crossrefs

Cf. A060773 (n having a unique partition into three nonnegative triangular numbers).

Cf. A002097, A064825.

Sequence in context: A173186 A335575 A047746 * A324334 A370600 A080262

Adjacent sequences: A111635 A111636 A111637 * A111639 A111640 A111641

Keyword

fini,full,nonn

Author

T. D. Noe, Aug 10 2005

Status

approved