cp's OEIS Frontend

A022178 Triangle of Gaussian binomial coefficients [ n,k ] for q = 14.

%I A022178 #18 Nov 26 2021 12:54:08
%S A022178 1,1,1,1,15,1,1,211,211,1,1,2955,41567,2955,1,1,41371,8150087,8150087,
%T A022178 41371,1,1,579195,1597458423,22371988815,1597458423,579195,1,1,
%U A022178 8108731,313102430103,61390334766783,61390334766783
%N A022178 Triangle of Gaussian binomial coefficients [ n,k ] for q = 14.
%D A022178 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H A022178 G. C. Greubel, <a href="/A022178/b022178.txt">Rows n = 0..50 of triangle, flattened</a>
%H A022178 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 A022178 T(n,k) = T(n-1,k-1) + q^k * T(n-1,k), with q=14. - _G. C. Greubel_, May 28 2018
%t A022178 Table[QBinomial[n,k,14], {n,0,10}, {k,0,n}]//Flatten (* or *) q:= 14; 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 A022178 (PARI) {q=14; 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 A022178 for(n=0,10, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 28 2018
%K A022178 nonn,tabl
%O A022178 0,5
%A A022178 _N. J. A. Sloane_