2002 AMC 10B Problem 23

Let \{a_k\} be a sequence of integers such that a_1=1 and a_{m+n}=a_m+a_n+mn, for all positive integers m and n. Then a_{12} is

\mathrm{(A) \ } 45\qquad \mathrm{(B) \ } 56\qquad \mathrm{(C) \ } 67\qquad \mathrm{(D) \ } 78\qquad \mathrm{(E) \ } 89

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.