|
|
A022181
|
|
Triangle of Gaussian binomial coefficients [ n,k ] for q = 17.
|
|
16
|
|
|
1, 1, 1, 1, 18, 1, 1, 307, 307, 1, 1, 5220, 89030, 5220, 1, 1, 88741, 25734890, 25734890, 88741, 1, 1, 1508598, 7437471951, 126461249460, 7437471951, 1508598, 1, 1, 25646167, 2149430902437, 621311556068931, 621311556068931
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
REFERENCES
|
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
|
|
LINKS
|
|
|
FORMULA
|
T(n,k) = T(n-1,k-1) + q^k * T(n-1,k), with q=17. - G. C. Greubel, May 28 2018
|
|
MATHEMATICA
|
Table[QBinomial[n, k, 17], {n, 0, 10}, {k, 0, n}]//Flatten (* or *) q:= 17; 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 *)
|
|
PROG
|
(PARI) {q=17; 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
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|