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

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

Author

Roger L. Bagula and Gary W. Adamson, Mar 28 2009

Keywords

• nonn
• easy
• tabl

Comments

Row sums are in A052905.

Examples

			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;
		

References

• H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, pp 159-162.

Crossrefs

Cf. A130303

Programs

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[%]

Formula

T(n,k) = n-k, k>=1. - R. J. Mathar, Jul 11 2012