A204202 - OEIS

%I #10 Dec 24 2013 01:52:27

%S 2,2,5,2,7,11,2,9,18,23,2,11,27,41,47,2,13,38,68,88,95,2,15,51,106,

%T 156,183,191,2,17,66,157,262,339,374,383,2,19,83,223,419,601,713,757,

%U 767,2,21,102,306,642,1020,1314,1470,1524,1535,2,23,123,408,948

%N Triangle based on (0,2/3,1) averaging array.

%C   See A204201 for a discussion of averaging arrays and related triangles

%F From _Philippe Deléham_, Dec 24 2013: (Start)

%F T(n,n) = A055010(n) = A083329(n) = A153893(n-1).

%F Sum_{k=1..n} T(n,k) = A066373(n+1).

%F T(n,k) = T(n-1,k)+3*T(n-1,k-1)-2*T(n-2,k-1)-2*T(n-2,k-2), T(1,1)=2, T(2,1)=2, T(2,2)=5, T(n,k)=0 if k<1 or if k>n. (End)

%e First six rows:

%e 2

%e 2...5

%e 2...7....11

%e 2...9....18...23

%e 2...11...27...41...47

%e 2...13...38...68...88..95

%t a = 0; r = 2/3; b = 1;

%t t[1, 1] = r;

%t t[n_, 1] := (a + t[n - 1, 1])/2;

%t t[n_, n_] := (b + t[n - 1, n - 1])/2;

%t t[n_, k_] := (t[n - 1, k - 1] + t[n - 1, k])/2;

%t u[n_] := Table[t[n, k], {k, 1, n}]

%t Table[u[n], {n, 1, 5}]   (* averaging array *)

%t u = Table[(1/r) 2^n*u[n], {n, 1, 12}];

%t TableForm[u]  (* A204202 triangle *)

%t Flatten[u]    (* A204202 sequence *)

%Y Cf. A204201.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Jan 12 2012