A new family of amicable Hadamard matrices

We study constructions for amicable Hadamard matrices. The family for orders 2t, t a positive integer is explicitly exhibited. We also show that there are amicable Hadamard matrices of order (2t-1)r + 1 for any odd integer r> 1. Now we have orders 15r + 1, 63r + 1, 255r + 1, 511 r + 1, ...., r> 1 an odd integer, for the first time.