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A022176 Triangle of Gaussian binomial coefficients [ n,k ] for q = 12. 16
1, 1, 1, 1, 13, 1, 1, 157, 157, 1, 1, 1885, 22765, 1885, 1, 1, 22621, 3280045, 3280045, 22621, 1, 1, 271453, 472349101, 5671197805, 472349101, 271453, 1, 1, 3257437, 68018541997, 9800302156141, 9800302156141 (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

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=12. - G. C. Greubel, May 29 2018

MATHEMATICA

Table[QBinomial[n, k, 12], {n, 0, 10}, {k, 0, n}]//Flatten (* or *) q:= 12; 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=12; 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

Sequence in context: A174694 A156539 A172300 * A188646 A174791 A015132

Adjacent sequences:  A022173 A022174 A022175 * A022177 A022178 A022179

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 10 23:29 EST 2019. Contains 329910 sequences. (Running on oeis4.)