what is the formula for this progression?

dinnu:

t= 3, 8,15, 24

(+5, +7, +9, +11 ..)

t( 1 ) = 3
t( 2 ) = 3+1+2*2 = 8
t( 3 ) = 8+1+3*2 = 15
t( 4 ) = 15+1+4*2 = 24

that's:
t( x ) = t( x-1 ) + 1+2*x for x>0 and t(0)=0