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%I #11 Jun 05 2018 02:42:39
%S 1,1,1,1,13,1,1,157,157,1,1,1885,22765,1885,1,1,22621,3280045,3280045,
%T 22621,1,1,271453,472349101,5671197805,472349101,271453,1,1,3257437,
%U 68018541997,9800302156141,9800302156141
%N Triangle of Gaussian binomial coefficients [ n,k ] for q = 12.
%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="/A022176/b022176.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=12. - _G. C. Greubel_, May 29 2018
%t Table[QBinomial[n,k,12], {n,0,10}, {k,0,n}]//Flatten (* or *) q:= 12; 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=12; 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_
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