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A204205 Triangle based on (0,1/5,1) averaging array.

%I A204205 #9 Dec 25 2013 02:30:45
%S A204205 1,1,6,1,7,16,1,8,23,36,1,9,31,59,76,1,10,40,90,135,156,1,11,50,130,
%T A204205 225,291,316,1,12,61,180,355,516,607,636,1,13,73,241,535,871,1123,
%U A204205 1243,1276,1,14,86,314,776,1406,1994,2366,2519,2556,1,15,100,400
%N A204205 Triangle based on (0,1/5,1) averaging array.
%C A204205 See A204201 for a discussion and guide to other averaging arrays.
%F A204205 T(n,n) = A048487(n-1). - _Philippe Deléham_, Dec 24 2013
%F A204205 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)=1, T(2,1)=1, T(2,2)=6, T(n,k)=0 if k<1 or if k>n. - _Philippe Deléham_, Dec 24 2013
%e A204205 First six rows:
%e A204205 1
%e A204205 1...6
%e A204205 1...7...16
%e A204205 1...8...23...36
%e A204205 1...9...31...59...76
%e A204205 1...10..40...90...135...156
%t A204205 a = 0; r = 1/5; b = 1;
%t A204205 t[1, 1] = r;
%t A204205 t[n_, 1] := (a + t[n - 1, 1])/2;
%t A204205 t[n_, n_] := (b + t[n - 1, n - 1])/2;
%t A204205 t[n_, k_] := (t[n - 1, k - 1] + t[n - 1, k])/2;
%t A204205 u[n_] := Table[t[n, k], {k, 1, n}]
%t A204205 Table[u[n], {n, 1, 5}]    (* averaging array *)
%t A204205 u = Table[(1/2) (1/r) 2^n*u[n], {n, 1, 12}];
%t A204205 TableForm[u]   (* A204205 triangle *)
%t A204205 Flatten[u]     (* A204205 sequence *)
%Y A204205 Cf. A204201.
%K A204205 nonn,tabl
%O A204205 1,3
%A A204205 _Clark Kimberling_, Jan 12 2012