equation and matrix calculus

I have a Aleat.xlsx table from I imported the integer value in D(15,6) => and construct a matrix in the first column we write the difference

DM(i,1) = D(i,1)-D(i+1,1); .... DM(i,10) = D(i,10)-D(i+1,10);

I have to calculus the coeficents a11, ...a10,1 from equations

b1 = DM(1,1)*a11+DM(1,2)*a21+DM(1,3)*a31+DM(1,4)*a41+DM(1,5)*a51+DM(1,6)*a61+DM(1,7)*a71+DM(1,8)*a81+DM(1,9)*a91+DM(1,10)*a101;

b10 = DM(10,1)*a11+DM(10,2)*a21+DM(10,3)*a31+DM(10,4)*a41+DM(10,5)*a51+DM(10,6)*a61+DM(10,7)*a71+DM(10,8)*a81+DM(10,9)*a91+DM(10,10)*a101;

the result in [a11 a21 ... a101];

We have to predict [a11 a21 ... a101] so b1 = D(1,1).. b10 = D(10,1); thus the line 11 of D(11,i) is equal with those calculus .

The program is of fixed lenght = 10 how can I modified the program thus D(n+5,6), b1...bn, a(11),.. a(n,1), in a loop for n integer >= 1000

so we shift the the calculus area from the first to n position until 2 to n+1 and the prediction of line n+2 and continue 5 steps with other coeficients . a(21),.. a(n+1,1) and find value a(n,n).

Practicly prom a set of n data to predict the n+1 value considering the order 1,2,3... differece multipplied with constant coefficient.

The program should be in some kind extensible with given n and to inspect the coeficient [a11 a21 ... an1]; to find the rule for an acurate prediction of the next value.

Please Help!

D = xlsread('Aleat.xlsx',1);
n = 10;
nCols = 10;
syms a11 a21 a31 a41 a51 a61 a71 a81 a91 a101;
M = zeros(n,n);
%filePath = 'Aleator.xlsx'
%data = readMatrixData(filePath);
%N = data(:,4);
M(1,1:n) = 0;
DM = zeros(10,10);
for i = 1:n
DM(i,1) = D(i,1)-D(i+1,1);
end;
for i = 1:(n-1)
DM(i,2) = DM(i,1)-DM(i+1,1);
end;
for i = 1:(n-2)
DM(i,3) = DM(i,2)-DM(i+1,2);
end;
for i = 1:(n-3)
DM(i,4) = DM(i,3)-DM(i+1,3);
end;
for i = 1:(n-4)
DM(i,5) = DM(i,4)-DM(i+1,4);
end;
for i = 1:(n-5)
DM(i,6) = DM(i,5)-DM(i+1,5);
end;
for i = 1:(n-6)
DM(i,7) = DM(i,6)-DM(i+1,6);
end;
for i = 1:(n-7)
DM(i,8) = DM(i,7)-DM(i+1,7);
end;
for i = 1:(n-8)
DM(i,9) = DM(i,8)-DM(i+1,8);
end;
for i = 1:(n-9)
DM(i,10) = DM(i,9)-DM(i+1,9);
end;
b1 = D(14,1);
b2 = D(13,1);
b3 = D(12,1);
b4 = D(11,1);
b5 = D(10,1);
b6 = D(9,1);
b7 = D(8,1);
b8 = D(7,1);
b9 = D(6,1);
b10 = D(5,1);
B1 = [b1 b2 b3 b4 b5 b6 b7 b8 b9 b10];
B2 = B1';
% We need to solve DM * a = b
% DM is (nRows - 1) x nCols matrix
% b is a column vector of size nCols
% Check if we have enough equations and variables
if size(DM, 1) < nCols
    error('Insufficient number of equations.');
end
% Solve for coefficients a
% We are solving DM * a = b
% Using left division to find a
%size(DM)
%size(B1)
a = DM' \ B1';
b1 = DM(1,1)*a11+DM(1,2)*a21+DM(1,3)*a31+DM(1,4)*a41+DM(1,5)*a51+DM(1,6)*a61+DM(1,7)*a71+DM(1,8)*a81+DM(1,9)*a91+DM(1,10)*a101;
b2 = DM(2,1)*a11+DM(2,2)*a21+DM(2,3)*a31+DM(2,4)*a41+DM(2,5)*a51+DM(2,6)*a61+DM(2,7)*a71+DM(2,8)*a81+DM(2,9)*a91+DM(2,10)*a101;
b3 = DM(3,1)*a11+DM(3,2)*a21+DM(3,3)*a31+DM(3,4)*a41+DM(3,5)*a51+DM(3,6)*a61+DM(3,7)*a71+DM(3,8)*a81+DM(3,9)*a91+DM(3,10)*a101;
b4 = DM(4,1)*a11+DM(4,2)*a21+DM(4,3)*a31+DM(4,4)*a41+DM(4,5)*a51+DM(4,6)*a61+DM(4,7)*a71+DM(4,8)*a81+DM(4,9)*a91+DM(4,10)*a101;
b5 = DM(5,1)*a11+DM(5,2)*a21+DM(5,3)*a31+DM(5,4)*a41+DM(5,5)*a51+DM(5,6)*a61+DM(5,7)*a71+DM(5,8)*a81+DM(5,9)*a91+DM(5,10)*a101;
b6 = DM(6,1)*a11+DM(6,2)*a21+DM(6,3)*a31+DM(6,4)*a41+DM(6,5)*a51+DM(6,6)*a61+DM(6,7)*a71+DM(6,8)*a81+DM(6,9)*a91+DM(6,10)*a101;
b7 = DM(7,1)*a11+DM(7,2)*a21+DM(7,3)*a31+DM(7,4)*a41+DM(7,5)*a51+DM(7,6)*a61+DM(7,7)*a71+DM(7,8)*a81+DM(7,9)*a91+DM(7,10)*a101;
b8 = DM(8,1)*a11+DM(8,2)*a21+DM(8,3)*a31+DM(8,4)*a41+DM(8,5)*a51+DM(8,6)*a61+DM(8,7)*a71+DM(8,8)*a81+DM(8,9)*a91+DM(8,10)*a101;
b9 = DM(9,1)*a11+DM(9,2)*a21+DM(9,3)*a31+DM(9,4)*a41+DM(9,5)*a51+DM(9,6)*a61+DM(9,7)*a71+DM(9,8)*a81+DM(9,9)*a91+DM(9,10)*a101;
b10 = DM(10,1)*a11+DM(10,2)*a21+DM(10,3)*a31+DM(10,4)*a41+DM(10,5)*a51+DM(10,6)*a61+DM(10,7)*a71+DM(10,8)*a81+DM(10,9)*a91+DM(10,10)*a101;
%c1 = 20;%
%B1 = zeros(n,1);

%X = linsolve(DM, B1);