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%I #8 Apr 27 2017 11:08:21
%S 1,2,1,2,1,1,2,1,0,1,2,1,1,-1,1,2,1,0,2,-2,1,2,1,1,-2,4,-3,1,2,1,0,3,
%T -6,7,-4,1,2,1,1,-3,9,-13,11,-5,1,2,1,0,4,-12,22,-24,16,-6,1,2,1,1,-4,
%U 16,-34,46,-40,22,-7,1,2,1,0,5,-20,50,-80,86,-62,29,-8,1,2,1,1,-5,25,-70,130,-166,148,-91,37,-9,1
%N Riordan array ((1+x)/(1-x),x/(1+x)).
%C Row sums are A113311. Diagonal sums are A113312. Inverse is A113313. The family of Riordan arrays ((1+x)/(1-(q-1)x),x/(1+x)) allow one to calculate the weight distribution of MDS codes.
%D F.J. MacWilliams, N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 2003, p. 321.
%F T(n, k)=sum{j=0..n-k, (-1)^j*C(j+k-2, i)}; T(n, k)=sum{j=0..n-k, (-1)^(n-k-j)C(n-j-2, n-j-k); T(n, k)=sum{j=k..n, (-1)^(n-j)*C(n, j)(2^(j-k+1)-1).
%e Triangle begins
%e 1;
%e 2,1;
%e 2,1,1;
%e 2,1,0,1;
%e 2,1,1,-1,1;
%e 2,1,0,2,-2,1;
%t T[n_, k_] := Sum[(-1)^(n-j) Binomial[n, j] (2^(j-k+1) - 1), {j, k, n}]; Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Apr 27 2017 *)
%K easy,sign,tabl
%O 0,2
%A _Paul Barry_, Oct 25 2005
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