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A158860
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.
1
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
OFFSET
1,2
COMMENTS
Row sums are in A052905.
REFERENCES
H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, pp 159-162.
FORMULA
T(n,k) = n-k, k>=1. - R. J. Mathar, Jul 11 2012
EXAMPLE
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;
MAPLE
A158860 := proc(n, k)
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;
end proc: # R. J. Mathar, Jul 11 2012
MATHEMATICA
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[%]
CROSSREFS
Sequence in context: A340073 A050356 A245838 * A335619 A037022 A037023
KEYWORD
nonn,easy,tabl
AUTHOR
STATUS
approved