A158860 - OEIS

%I #5 Jul 11 2012 11:24:36

%S 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,

%T 4,3,2,1,25,8,7,6,5,4,3,2,1,28,9,8,7,6,5,4,3,2,1

%N 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.

%C Row sums are in A052905.

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

%F T(n,k) = n-k, k>=1. - _R. J. Mathar_, Jul 11 2012

%e 1;

%e 4, 1;

%e 7, 2, 1;

%e 10, 3, 2, 1;

%e 13, 4, 3, 2, 1;

%e 16, 5, 4, 3, 2, 1;

%e 19, 6, 5, 4, 3, 2, 1;

%e 22, 7, 6, 5, 4, 3, 2, 1;

%e 25, 8, 7, 6, 5, 4, 3, 2, 1;

%e 28, 9, 8, 7, 6, 5, 4, 3, 2, 1;

%p A158860 := proc(n,k)

%p     option remember;

%p     if k = 0 then

%p         3*n-2 ;

%p     elif k >= n then

%p         0 ;

%p     else

%p         (1+procname(n-1,k)*procname(n,k-1))/procname(n-1,k-1) ;

%p     end if;

%p end proc: # _R. J. Mathar_, Jul 11 2012

%t Clear[e, n, k];

%t e[n_, 0] := 3*n - 2;

%t e[n_, k_] := 0 /; k >= n;

%t e[n_, k_] := (e[n - 1, k]*e[n, k - 1] + 1)/e[n - 1, k - 1];

%t Table[Table[e[n, k], {k, 0, n - 1}], {n, 1, 10}];

%t Flatten[%]

%Y Cf. A130303

%K nonn,easy,tabl

%O 1,2

%A _Roger L. Bagula_ and _Gary W. Adamson_, Mar 28 2009