Contribution_NF

Limit the search to triplets less than 1,000 (that is, to a maximum of 987, 988, 989).
*/
autodefine "off"
openconsole
color 15,0
int count, sum, i, product
sum = 0
count = 0
print "First   Second Third   Triangular      Product"
print "i       i+1     i+2     Place           i(i+1)(i+2)"
print "====== ====== ====== ============== ==========="
' Start from -2 as Sloanes [http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A000217]
' lists 0 as a triangular number
for i = -2 to 997
product = i*(i+1)*(i+2)
while sum<product
   count++
   sum = sum + count
endwhile
if product = sum
   print i,"\t",i+1,"\t",i+2,"\t",count,"\t\t",sum
endif
next i

locate 25,35 : print "Finished.",
do : until inkey$<>""
closeconsole
end

/*
Output
First      Second   Third       Triangular             Product
i             i+1       i+2           Place          i(i+1)(i+2)
====== ====== ====== ============== ===========
   -2        -1          0        0                  0
       -1             0                1        0                0
         0    1         2       0                    0
        1     2       3         3                    6
        4         5     6         15               120
        5     6     7                     20             210
        9           10       11          44               990
      56       57   58        608                185136
    636    637   638        22736       258474216
*/

Thanks for the input. Your answers are correct. I never considered using 0 as a triangular number! So I missed the first three solutions which you printed out. I've mentioned this in the Puzzlet webpage and given you the credit.

Note that we both used different methods for detecting triangularity on this occasion as well.