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A022180 Triangle of Gaussian binomial coefficients [ n,k ] for q = 16. 16

%I

%S 1,1,1,1,17,1,1,273,273,1,1,4369,70161,4369,1,1,69905,17965585,

%T 17965585,69905,1,1,1118481,4599259665,73605001745,4599259665,1118481,

%U 1,1,17895697,1177411592721,301490686407185,301490686407185

%N Triangle of Gaussian binomial coefficients [ n,k ] for q = 16.

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

%D Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

%H G. C. Greubel, <a href="/A022180/b022180.txt">Rows n=0..50 of triangle, flattened</a>

%F T(n,k) = T(n-1,k-1) + q^k * T(n-1,k), with q=16. - _G. C. Greubel_, May 28 2018

%t Table[QBinomial[n,k,16], {n,0,10}, {k,0,n}]//Flatten (* or *) q:= 16; 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=16; 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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Last modified April 19 22:22 EDT 2019. Contains 322291 sequences. (Running on oeis4.)