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A022180
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Triangle of Gaussian binomial coefficients [ n,k ] for q = 16.
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17
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1, 1, 1, 1, 17, 1, 1, 273, 273, 1, 1, 4369, 70161, 4369, 1, 1, 69905, 17965585, 17965585, 69905, 1, 1, 1118481, 4599259665, 73605001745, 4599259665, 1118481, 1, 1, 17895697, 1177411592721, 301490686407185, 301490686407185
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OFFSET
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0,5
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REFERENCES
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F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
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LINKS
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FORMULA
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T(n,k) = T(n-1,k-1) + q^k * T(n-1,k), with q=16. - G. C. Greubel, May 28 2018
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MATHEMATICA
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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 *)
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PROG
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(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))))};
for(n=0, 10, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, May 28 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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