[seqfan] A006451 = n such that n*(n+1)/2+1 is square?

[Joerg Arndt]

with seq:
A006451 Solution to a diophantine equation. 
it would be nice to state the Diophantine eqn.

It appears that
A006451 = n such that n*(n+1)/2+1 is square

? for(n=1,10000,t=n*(n+1)/2+1;if(issquare(t), print1(n,", ")))
2, 5, 15, 32, 90, 189, 527, 1104, 3074, 6437,

We have n*(n+1)/2+1 as entry
A000124 Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1


Some Diophantinista may want to enter seq
k such that n*(n+1)+k can be square.
(might be unworthy if trivial for some reason).
Quick & dirty:
? for(k=0,20,q=0;for(n=1,10000,t=n*(n+1)/2+k;if(issquare(t),q=1;break())); if(q, print1(k,", ")))
0, 1, 3, 4, 6, 8, 9, 10, 13, 15, 16, 19, 
seq. not in OEIS, neither complement,
neither for negative k.