In the song “The Twelve Days of Christmas,” gifts are sent on successive days according to...

In the song “The Twelve Days of Christmas,” gifts are sent on successive days according to the following pattern:

First day: A partridge in a pear tree.

Second day. Two turtledoves and another partridge.

Third day: Three French hens, two turtledoves, and a partridge And so on.

For each i = 1,…,12, let gi be the number of gifts sent on the ith day. Then g1 = 1, and for i = 2,…,12 we have

gi = gi − 1 + i.

Now let tn be the total number of gifts sent during the first n days of Christmas. Find a formula for tn in the form

,

where a, b,c ∈ ℕ.