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

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

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

G. C. Greubel, Rows n=0..50 of triangle, flattened

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

Formula

T(n,k) = T(n-1,k-1) + q^k * T(n-1,k), with q=16. - G. C. Greubel, May 28 2018

Mathematica

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 *)

Prog

(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

Crossrefs

Row sums give A015204.

Sequence in context: A157151 A176794 A176244 * A156581 A015143 A172196

Adjacent sequences: A022177 A022178 A022179 * A022181 A022182 A022183

Keyword

nonn,tabl

Author

N. J. A. Sloane

Status

approved