Sum[Floor[(a*i*(-3+2*i)+b)/m], {i, 1, n}] in closed algebraic form and output.

def sum_of_seq(a, b, m, n):
  return (a*n*(n+1)*(2*n+1)/6) - (a*n*(n+1)*(n-1)/2) + (a*b*n/m) + (b*n*(n+1)/2)

sum_of_seq(1, 2, 3, 4)