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A204206 Triangle based on (1,3/2,2) averaging array.

%I A204206 #9 Dec 25 2013 02:31:32
%S A204206 3,5,7,9,12,15,17,21,27,31,33,38,48,58,63,65,71,86,106,121,127,129,
%T A204206 136,157,192,227,248,255,257,265,293,349,419,475,503,511,513,522,558,
%U A204206 642,768,894,978,1014,1023,1025,1035,1080,1200,1410,1662,1872
%N A204206 Triangle based on (1,3/2,2) averaging array.
%C A204206 See A204201 for a discussion and guide to other averaging arrays.
%F A204206 From _Philippe Deléham_, Dec 24 2013: (Start)
%F A204206 T(n,n) = A000225(n+1).
%F A204206 Sum_{k=1..n} T(n,k) = A167667(n).
%F A204206 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)=3, T(2,1)=5, T(2,2)=7, T(n,k)=0 if k<1 or if k>n. (End)
%e A204206 First six rows:
%e A204206 3
%e A204206 5...7
%e A204206 9...12...15
%e A204206 17..21...27...31
%e A204206 33..38...48...58...63
%e A204206 65..71...86...106..121..127
%t A204206 a = 1; r = 3/2; b = 2;
%t A204206 t[1, 1] = r;
%t A204206 t[n_, 1] := (a + t[n - 1, 1])/2;
%t A204206 t[n_, n_] := (b + t[n - 1, n - 1])/2;
%t A204206 t[n_, k_] := (t[n - 1, k - 1] + t[n - 1, k])/2;
%t A204206 u[n_] := Table[t[n, k], {k, 1, n}]
%t A204206 Table[u[n], {n, 1, 5}]    (* averaging array *)
%t A204206 u = Table[3 (1/2) (1/r) 2^n*u[n], {n, 1, 12}];
%t A204206 TableForm[u]   (* A204206 triangle *)
%t A204206 Flatten[u]     (* A204206 sequence *)
%Y A204206 Cf. A204201.
%K A204206 nonn,tabl
%O A204206 1,1
%A A204206 _Clark Kimberling_, Jan 12 2012