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A022174
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Triangle of Gaussian binomial coefficients [ n,k ] for q = 10.
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17
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1, 1, 1, 1, 11, 1, 1, 111, 111, 1, 1, 1111, 11211, 1111, 1, 1, 11111, 1122211, 1122211, 11111, 1, 1, 111111, 112232211, 1123333211, 112232211, 111111, 1, 1, 1111111, 11223332211, 1123445443211, 1123445443211
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listen;
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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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EXAMPLE
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1 ;
1 1;
1 11 1;
1 111 111 1;
1 1111 11211 1111 1;
1 11111 1122211 1122211 11111 1;
1 111111 112232211 1123333211 112232211 111111 1;
1 1111111 11223332211 1123445443211 1123445443211 11223332211 1111111 1;
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MAPLE
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mul(10^i-1, i=1..n) ;
end proc:
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MATHEMATICA
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a027878[n_]:=Times@@ Table[10^i - 1, {i, n}]; T[n_, m_]:=a027878[n]/( a027878[m] a027878[n - m]); Table[T[n, m], {n, 0, 10}, {m, 0, n}]//Flatten (* Indranil Ghosh, Jul 20 2017, after Maple code *)
Table[QBinomial[n, k, 10], {n, 0, 10}, {k, 0, n}]//Flatten (* or *) q:= 10; 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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(Python)
from operator import mul
def a027878(n): return 1 if n==0 else reduce(mul, [10**i - 1 for i in range(1, n + 1)])
def T(n, m): return a027878(n)/(a027878(m)*a027878(n - m))
for n in range(11): print([T(n, m) for m in range(n + 1)]) # Indranil Ghosh, Jul 20 2017, after Maple code
(PARI) {q=10; 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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