%I #11 May 13 2019 08:48:38

%S 1,1,1,1,12,1,1,133,133,1,1,1464,16226,1464,1,1,16105,1964810,1964810,

%T 16105,1,1,177156,237758115,2617126920,237758115,177156,1,1,1948717,

%U 28768909071,3483633688635,3483633688635

%N Triangle of Gaussian binomial coefficients [ n,k ] for q = 11.

%D F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.

%H G. C. Greubel, <a href="/A022175/b022175.txt">Rows n=0..50 of triangle, flattened</a>

%H Kent E. Morrison, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

%F T(n,k) = T(n-1,k-1) + q^k * T(n-1,k), with q=11. - _G. C. Greubel_, May 28 2018

%t Table[QBinomial[n,k,11], {n,0,10}, {k,0,n}]//Flatten (* or *) q:= 11; T[n_, 0]:= 1; T[n_,n_]:= 1; T[n_,k_]:= T[n,k] = If[k < 0 || n < k, 0, T[n-1, k -1] +q^k*T[n-1,k]]; Table[T[n,k], {n,0,10}, {k,0,n}] // Flatten (* _G. C. Greubel_, May 28 2018 *)

%o (PARI) {q=11; T(n,k) = if(k==0,1, if (k==n, 1, if (k<0 || n<k, 0, T(n-1,k-1) + q^k*T(n-1,k))))};

%o for(n=0,10, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 28 2018

%K nonn,tabl

%O 0,5

%A _N. J. A. Sloane_