Crud, seem to have duplicated linear relations... trying again... Here are relations involving a[1]: 1*a[1]+1*a[2]-6*a[3]-8*a[4]-8*a[5] = -0.0000000000000002 1*a[1]-1*a[2]-4*a[3]-4*a[4]-4*a[5] = -0.0000000000000000 1*a[1]-2*a[2]-3*a[3]-2*a[4]-2*a[5] = -0.0000000000000000 1*a[1]-3*a[2]-2*a[3] = -0.0000000000000000 1*a[1]-3*a[2]-2*a[4]-4*a[6]-4*a[7] = -0.0000000000000000 1*a[1]-4*a[2]-1*a[3]+2*a[4]+2*a[5] = 0.0000000000000000 1*a[1]-5*a[2]+4*a[4]+4*a[5] = -0.0000000000000000 1*a[1]-5*a[2]+8*a[4]-8*a[8]-8*a[9] = -0.0000000000000000 1*a[1]-5*a[2]+8*a[5]+8*a[8]+8*a[9] = -0.0000000000000000 1*a[1]-5*a[3]-6*a[4]-6*a[5] = -0.0000000000000001 1*a[1]-6*a[2]+1*a[3]+6*a[4]+6*a[5] = 0.0000000000000000 1*a[1]-7*a[2]+2*a[3]+8*a[4]+8*a[5] = 0.0000000000000001 2*a[1]-3*a[2]-7*a[3]-6*a[4]-6*a[5] = -0.0000000000000001 2*a[1]-5*a[2]-5*a[3]-2*a[4]-2*a[5] = -0.0000000000000001 2*a[1]-7*a[2]-3*a[3]+2*a[4]+2*a[5] = 0.0000000000000000 3*a[1]-7*a[2]-8*a[3]-4*a[4]-4*a[5] = 0.0000000000000001 3*a[1]-8*a[2]-7*a[3]-2*a[4]-2*a[5] = 0.0000000000000001 Here are some involving a[2] but not a[1]: 1*a[2]-1*a[3]-2*a[4]-2*a[5] = -0.0000000000000000 1*a[2]-1*a[3]-4*a[4]+4*a[8]+4*a[9] = -0.0000000000000000 1*a[2]-1*a[3]-4*a[5]-4*a[8]-4*a[9] = -0.0000000000000000 1*a[2]-3*a[3]-2*a[5]+4*a[6]+4*a[7] = -0.0000000000000000 1*a[2]-3*a[4]-2*a[5]-2*a[6]-2*a[7] = -0.0000000000000000 Here are some involving a[3] but not a[1],a[2]: 1*a[3]-1*a[4]-2*a[6]-2*a[7] = 0.0000000000000000 1*a[3]-1*a[4]-4*a[6]+4*a[12]+4*a[13] = 0.0000000000000000 1*a[3]-1*a[4]-4*a[7]-4*a[12]-4*a[13] = 0.0000000000000000 Here are some involving a[4] but not a[1,2,3]: 1*a[4]-1*a[5]-2*a[8]-2*a[9] = 0.0000000000000000 1*a[4]-1*a[5]-4*a[8]+4*a[16]+4*a[17] = 0.0000000000000000 1*a[4]-1*a[5]-4*a[9]-4*a[16]-4*a[17] = 0.0000000000000000 And... 1*a[5]-1*a[6]-2*a[10]-2*a[11] = 0.0000000000000000 1*a[5]-1*a[6]-4*a[10]+4*a[20]+4*a[21] = 0.0000000000000000 1*a[5]-1*a[6]-4*a[11]-4*a[20]-4*a[21] = 0.0000000000000000 Here are some relations involving b[1]: 1*b[1]-3*b[2]-6*b[3]-8*b[4]-8*b[5] = 0.0000000000000001 1*b[1]-4*b[2]-5*b[3]-4*b[4]-4*b[5] = 0.0000000000000001 1*b[1]-5*b[2]-4*b[3] = 0.0000000000000002 1*b[1]-6*b[2]-3*b[3]+4*b[4]+4*b[5] = 0.0000000000000001 1*b[1]-7*b[2]-2*b[3]+8*b[4]+8*b[5] = 0.0000000000000001 But it appears they all are consequences of just one of them and 1*b[2]-1*b[3]-4*b[4]-4*b[5] = -0.0000000000000000 We also have 1*b[2]-5*b[4]-4*b[5]-4*b[6]-4*b[7] = -0.0000000000000000 But it arises from 1*b[3]-1*b[4]-4*b[6]-4*b[7] = -0.0000000000000000 and there is 1*b[4]-1*b[5]-4*b[8]-4*b[9] = 0.0000000000000000 1*b[5]-1*b[6]-4*b[10]-4*b[11] = 0.0000000000000000 1*b[6]-1*b[7]-4*b[12]-4*b[13] = 0.0000000000000000 1*b[7]-1*b[8]-4*b[14]-4*b[15] = 0.0000000000000000 Anyhow... the prime question would seem to be: What is the minimum number of constants you need to know, to be able to know all of a[1], a[2],..., a[N] since they all are just integer linear combinations of members of your master set? Certainly if N>0 the answer is at most ceiling((N+1)/2), from the Gosper-Hunt relations; and all of my relations for a[] listed above only determine a[2k]+a[2k+1] and not a[2k+1] alone, which suggests perhaps the Gosper-Hunt relations might be a full basis for the relations obeyed by a[].