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A158860
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Triangle T(n,k)= ( 1 +T(n-1,k)*T(n,k-1) ) / T(n-1,k-1) initialized by T(n,0)=3n-2, T(n,k)=0 if k>=n, read by rows 0<=k<n.
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1
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1, 4, 1, 7, 2, 1, 10, 3, 2, 1, 13, 4, 3, 2, 1, 16, 5, 4, 3, 2, 1, 19, 6, 5, 4, 3, 2, 1, 22, 7, 6, 5, 4, 3, 2, 1, 25, 8, 7, 6, 5, 4, 3, 2, 1, 28, 9, 8, 7, 6, 5, 4, 3, 2, 1
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, pp 159-162.
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LINKS
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FORMULA
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EXAMPLE
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1;
4, 1;
7, 2, 1;
10, 3, 2, 1;
13, 4, 3, 2, 1;
16, 5, 4, 3, 2, 1;
19, 6, 5, 4, 3, 2, 1;
22, 7, 6, 5, 4, 3, 2, 1;
25, 8, 7, 6, 5, 4, 3, 2, 1;
28, 9, 8, 7, 6, 5, 4, 3, 2, 1;
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MAPLE
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option remember;
if k = 0 then
3*n-2 ;
elif k >= n then
0 ;
else
(1+procname(n-1, k)*procname(n, k-1))/procname(n-1, k-1) ;
end if;
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MATHEMATICA
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Clear[e, n, k];
e[n_, 0] := 3*n - 2;
e[n_, k_] := 0 /; k >= n;
e[n_, k_] := (e[n - 1, k]*e[n, k - 1] + 1)/e[n - 1, k - 1];
Table[Table[e[n, k], {k, 0, n - 1}], {n, 1, 10}];
Flatten[%]
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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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