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A204202 Triangle based on (0,2/3,1) averaging array.

%I A204202 #10 Dec 24 2013 01:52:27
%S A204202 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 A204202 156,183,191,2,17,66,157,262,339,374,383,2,19,83,223,419,601,713,757,
%U A204202 767,2,21,102,306,642,1020,1314,1470,1524,1535,2,23,123,408,948
%N A204202 Triangle based on (0,2/3,1) averaging array.
%C A204202   See A204201 for a discussion of averaging arrays and related triangles
%F A204202 From _Philippe Deléham_, Dec 24 2013: (Start)
%F A204202 T(n,n) = A055010(n) = A083329(n) = A153893(n-1).
%F A204202 Sum_{k=1..n} T(n,k) = A066373(n+1).
%F A204202 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 A204202 First six rows:
%e A204202 2
%e A204202 2...5
%e A204202 2...7....11
%e A204202 2...9....18...23
%e A204202 2...11...27...41...47
%e A204202 2...13...38...68...88..95
%t A204202 a = 0; r = 2/3; b = 1;
%t A204202 t[1, 1] = r;
%t A204202 t[n_, 1] := (a + t[n - 1, 1])/2;
%t A204202 t[n_, n_] := (b + t[n - 1, n - 1])/2;
%t A204202 t[n_, k_] := (t[n - 1, k - 1] + t[n - 1, k])/2;
%t A204202 u[n_] := Table[t[n, k], {k, 1, n}]
%t A204202 Table[u[n], {n, 1, 5}]   (* averaging array *)
%t A204202 u = Table[(1/r) 2^n*u[n], {n, 1, 12}];
%t A204202 TableForm[u]  (* A204202 triangle *)
%t A204202 Flatten[u]    (* A204202 sequence *)
%Y A204202 Cf. A204201.
%K A204202 nonn,tabl
%O A204202 1,1
%A A204202 _Clark Kimberling_, Jan 12 2012