1,1

The Mathematica program first computes A024940, the number of partitions of n into distinct triangular numbers. Then it finds those n having zero such partitions. It appears that A024940 grows exponentially, which would preclude additional terms in this sequence. - T. D. Noe (noe(AT)sspectra.com), Jul 24 2006, Jan 05 2009

Joe Roberts, Lure of the Integers, page 184, entry 33.

David Wells in "The Penguin Dictionary of Curious and Interesting Numbers, Revised Edition, page 94, states that "33 is the largest number that is not the sum of distinct triangular numbers".

a(2) = 5: the 7 partitions of 5 are 5, 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1, 1+1+1+1+1. Among those the distinct ones are 5, 4+1, 3+2. None contains all distinct triangular numbers.

12 is a term as it is not a sum of 1, 3, 6 or 10 taken at most once.

nn=100; t=Rest[CoefficientList[Series[Product[(1+x^(k*(k+1)/2)), {k, nn}], {x, 0, nn(nn+1)/2}], x]]; Flatten[Position[t, 0]] - T. D. Noe (noe(AT)sspectra.com), Jul 24 2006

Complement of A061208.

Cf. A000217, A002243, A002244, A014134, A014156, A014158, A020757, A050941, A050942, A051611, A007294, A051533, A060773.

Sequence in context: A049633 A066614 A045746 this_sequence A004711 A000789 A076145

Adjacent sequences: A053611 A053612 A053613 this_sequence A053615 A053616 A053617

fini,full,nonn

Jud McCranie (j.mccranie(AT)comcast.net), Mar 19 2000

Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Jul 23 2006